The Gunners ran out 2-1 winners on the day as the Spaniard watched from the bench for 61 minutes before coming on to replace Nemanja Matic.
The 30-year-old started four of the Blues’ last six Premier League games as Antonio Conte’s men secured the title with a win over West Brom.
And he was unimpressed at being overlooked for the FA Cup final.
“I thought I was playing very, very well in the last few months,” explained Fabregas.
“I was in great form and it was a shame I didn’t start the game. I was playing very well and the team was winning, scoring a lot of goals and defending well.
“That is football, you have to accept decisions. It is a bad day and a shame because we wanted to win. The most important thing is the team didn’t win.
“Sometimes it is all about the coach’s decision. I don’t think I could have done much more this season, it is the coach’s decision and you have to respect that.
“I’m sure he wants the best for the team and if he thinks that is the way to go you have to go with it, we are a team. It is between him and me. I have nothing against Antonio, he has done a fantastic job.
“Of course every player wants to play more, it is in the genes of a winner and I am one of them. I’m here for whatever the team needs and I have shown that during the season.”
Fabregas, who started just 15 games for Chelsea this season, refused to rule out a move away from the club in the summer.
When asked if his lack of game time has made him think about leaving, he said: “Not necessarily, but in football you can never say never.
“Anything can happen but I have always said I feel very, very loved by the fans here and every time I have played I have shown I can play at the top level in this team. It is all about trying to change the manager’s decision.
“It is still a good season. We go home with a bad taste because of what has happened but for sure we would rather win the Premier League than the FA Cup.”
As was to be expected, the Spaniard was jeered by the Arsenal fans at Wembley, but spoke about the future of his old club under Arsene Wenger.
“I will speak about his [Wenger’s] legacy when he stops training,” said Fabregas.
“I don’t think that is the case [at the moment], I think he can manage for a long time. Let’s not take anything away from Arsenal, they were better than us and reacted well against 10 men.
“They scored and it made it very difficult because we were tired, the pitch is big and they have good passers of the ball.”