Madley threatened to send the Liverpool boss to the stands for erupting over tackles on the Reds playmaker, first from Islam Slimani then midfielder Matty James.
The Reds’ German boss was furious at the challenges on the Brazilian, who continues to be linked with a big-money move to Barcelona.
Klopp said: “What can I do? Write a letter saying ‘By the way, that’s a foul – next time can you whistle?’
“Even in the pre-season and even though it’s a Premier League tournament, we should talk about this. I was not too happy about two decisions around Phil Coutinho, one hundred percent.
“The ref told me that if I behave like I behaved today then I would have to go in the stands.
“I said: ‘If I behave like today then I go in the stand, no problem. But you have to change how you whistle’. For me, it was a clear foul, 100 per cent. It’s dangerous.
“It’s a difficult game to whistle for refs, I know all this.
“But these things are obvious for me and that’s why I thought it would be nice if he could help the players a little bit more because these players make the difference and these players bring people into the stadium.
“That’s why we have to look after them a little bit.”
Leicester took a 12th minute lead, when Slimani powered a header past Reds stopper Loris Karius.
Mohamed Salah equalised eight minutes later, before Coutinho’s stunning effort handed Liverpool victory in Hong Kong.
Antonio Conte has demanded Chelsea back him with a major summer spree – or risk another disastrous title defence.
The arrival of Alvaro Morata from Real Madrid will take Chelsea’s spending to £140million but Conte maintains it is still not enough.
The Blues boss wants Swansea striker Fernando Llorente, plus full-backs Alex Sandro from Juventus and Real’s Danilo.
He said: “We are a great club but we are in a moment where we can’t make a mistake.
“We need to improve and increase our squad and to be something important for the present but also for our future.
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“We must improve with new buys. To try to reach the same level of the other teams who stayed at the top. But they are working with these players for many years.
“Now we have to try to create this space [from the rest], to create these players to have 15 or 16 players and then every season we must add one piece, two piece to create a team ready to always stay at the top.
“We have to create solid foundations for this club.
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“Last season I utilised only 13 players regularly and we won the league and arrived at the final of the FA Cup.
“You can see that only 13 players made more than 10 appearances last season and it means that we have to improve our squad but my club knows this very well and we have to try to find the best solution.”
Conte has also insisted he is comfortable with his new contract with improved pay of £10m a year but no extension.
He added: “I always told you when we finished last season that I have two years’ contract to go.
“And then I thought this is the right way, to continue to give me motivation, to give the club motivation.”
Real were expected to make a fresh approach for long-time target De Gea this summer, after missing out on him on deadline day in 2015.
But Mourinho said Real had not followed up their long-term interest in De Gea and that the player himself had cooled on a move back to his native Spain.
“I can guarantee he’s not going this season, that I can,” said Mourinho.
“My feeling is it will be very difficult for him to go. He’s a very honest boy, very straight.
“He was contacted for a long time, the club was closed, then we opened, because I always have this feeling when a player has a desire to go, I don’t like to stop them because, in the end, you don’t get what you expect.
“So we opened it and then I decided to close, and the feeling from him is really, really good, I see him happy and 100 per cent he stays with us.”
Mourinho also revealed De Gea admitted having Sergio Romero as his understudy had made him a better keeper and forced him to raise his level.
“I think the best thing that could have happened to David was the way Romero played last season,” said Mourinho.
“Until then, David was clearly a safe man, a safe choice, and after what Romero did last season, David thinks he’s training in another way and David is much better now than before.
“He has amazing conditions in which to impress and to have both at the level they can be is fantastic for me.
“I will choose the players in relation to the moment, the qualities of the opponent and for Joel Pereira [United No.3] to be learning with them and playing with us is good.”
Mourinho is desperate to add at least one more player to his squad before the new season starts, but acknowledged the difficulty in getting deals over the line.
“Names are difficult for me, because the players belong to clubs, the players are in their seasons, and the managers and the owners are not happy if you speak about them, the same as me,” said Mourinho.
“If somebody says I want to buy a player from Manchester United, I would ask, hey, I’m here. So be careful what you say.
“I don’t hide my plans from the team, because the transfer window last January I didn’t use, and I told them my plan was to get four players and give balance to the team to make a better squad.
But I was getting the feedback from Mr Woodward [United executive vice-chairman], I was analysing myself from a distance, because I never got involved, but I repeat the same: the market is very difficult and if the club has no chance to give me the four players then so be it.
“I like my group and my players, and I go with them, but I still have the hope I can have a third player, maybe a fourth.”
One was captioned “F*** you China” and another of a sleeping security guard was tagged: “Wake up China. You idiot.”
Chinese fans accused the 21-year-old of xenophobia and racism, leading to an apology from the player.
“Hello my friends, just wanna say sorry if someone was sad because I used the expression “porra”, was no racism, just an expression…big hug” the player posted following Saturday’s game.
Now the Blues have seen fit to offer their own apology for the player’s actions, declaring “his behaviour does not represent the entire team and does not align with the club’s high expectations and strict requirements of its young players.”
They have also declared the player has been “strongly reprimanded and disciplined”.
A statement from the Blues declared:
“On July 22nd, Chelsea Football Club experienced the warmth and friendliness of Chinese fans at the National Stadium. However, we were surprised and disappointed that one day prior to the match, one of our young players, Kenedy, posted messages on his social media account that caused great offence and hurt the feelings of the people of China.
“Unfortunately, even though he quickly deleted the messages and apologised, and the club also apologised via our Chinese social media channels, the damage had already been done. Chelsea Football Club once again solemnly and sincerely apologises.
“Kenedy’s actions were a mistake that he will learn greatly from. His behaviour does not represent the entire team and does not align with the club’s high expectations and strict requirements of its young players. He has been strongly reprimanded and disciplined.
“Everyone at Chelsea Football Club has the utmost respect and admiration for China and loves our Chinese fans. It is because of this that the negative impact we have seen over the last two days has left us shocked and saddened. Once again, we sincerely apologise for the hurt caused to our Chinese fans as well as to the Chinese people.
“The match was a great cultural exchange event between China and Britain and the club is extremely grateful to China for its hospitality, which has brought us closer together in friendship. We very much hope to build on our strong relationship with our Chinese fans and friends, joining hands firmly with China in future for further cooperation
“We offer this apology with utmost sincerity. We have listened carefully to the criticism and will use the lessons learnt over the last two days to improve our processes in future.”
Kenedy and Chelsea arrived in Singapore for the next leg of their tour on Sunday.