Manchester City were held at the Etihad by the Red Devils in the goalless affair as the race for the top four tightens up.
The Spaniard was impressed by Carrick, who reciprocated the respect towards the manager of United’s bitter rivals.
“He said congratulations and well played. He’s obviously a terrific manager, he’s had success wherever he’s been and I have a lot of respect for him.”
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Pep Guardiola speaks ahead of Manchester derby
Carrick prompted a glowing tribute from the man who has overseen such talents as Xavi, Andres Iniesta and Xabi Alonso.
He said: “I am a big fan of Michael Carrick.
“He is one of the best holding midfielders I’ve ever seen in my life by far.
“He’s the level of Xabi Alonso, Sergio Busquets in Barcelona and Munich.
“All of them (United’s English players) they are perfect.
“Rashford is a big talent, of course, and Lingard.
“England is safe, you have outstanding players.
“Not just here in City – United, Tottenham, Chelsea. Come on guys – you can do it, the international team.”
Finding the man to fill Carrick’s shoes will be crucial to exploiting Pogba’s talent to the fullest.
He never looked better than when anchored by Andrea Pirlo at Juventus – and his performances have been enhanced when Carrick is in the United team.
Despite a difficult return to United this season, Guardiola has no doubts about the quality of a player City were so keen to sign two summers ago.
“I met Paul Pogba for the first time when Bayern Munich played Juventus last season,” said Guardiola. “In both games I was really impressed.
“He played in 10 positions. He is an outstanding player and he can do absolutely everything.
“Sometimes it’s not easy to handle the expectations you have when you arrive here, especially with the amount of money, it wasn’t easy.
“I think he made a good season.”