The midfielder, 30, was on the bench before being brought on in the 61st minute as Chelsea lost 2-1 at Wembley.
He started just 15 games for Chelsea this season, four of them in their past six Premier League games, to help the Blues win a sixth top-flight title.
“I was in great form and it was a shame I didn’t start the game,” he said.
“I thought I was playing very, very well in the last few months.
“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.
“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.”
Fabregas, who joined the Blues in 2014 from Barcelona, made 37 appearances in all competitions in Antonio Conte’s first season as manager.
The Spaniard, who helped Arsenal win the FA Cup in 2005, said he would “never say never” about leaving Chelsea.
“Anything can happen but I have always said I feel very, very loved by the fans here. It is all about trying to change the manager’s decision,” he added.