Arsenal finished fifth in the league, having crashed out of the Champions League following a 10-2 aggregate defeat to Bayern Munich.
Arsenal manager Arsene Wenger has reportedly already agreed the terms of his two-year contract extension.
Moses was sent off for a second bookable offence in the 68th minute after he went down in the Arsenal penalty area under the mere suggestion of contact from Alex Oxlade-Chamberlain.
He said more light would be shed on his situation on Wednesday or Thursday, but there seems little doubt Wenger is still held in high regard by the players.
"I've played until the end of my contract, which is today basically". Sometimes I think it could be tiredness'.
"For once I have taken my medal so that means it's a special night for me". The Arsenal manager, however, said he was keeping this one because it was the record-breaking seventh, and intimated this win was all the sweeter because of the doubt he suffered when Diego Costa equalised Alexis Sanchez's controversial opening goal, just before Aaron Ramsey headed the victor to deny Chelsea a league and FA Cup double. It is between him and me.
Wenger has been under a lot of criticism during the season, and after 21 years at the club, many vocal Arsenal supporters believe it is time for a change.
"I invite you one day to live with me and one thing you can not question is my commitment".
"It's been an up and down season", Ramsey said, "but to finish it with an FA Cup has to be a successful season".
Chelsea manager Antonio Conte were unhappy with the first goal. Banners with those words have been seen not only at Arsenal games, but at tennis tournaments and other soccer games all over the world, as disgruntled Gunners fans voice their displeasure with the Frenchman. We play for the 99.9 per cent. It's the board who has to decide who will lead the club in the future.
"Honestly. I think that this goal (should have been) disallowed because there is a clear handball".
Victory in this game after all came after a fine recent winning run, and from the type of bold decision that no-one thought Wenger capable: a sweeping and decisive tactical switch, as he moved to three at the back.
With Laurent Koscielny banned and Gabriel and Shkodran Mustafi injured, Wenger called on club captain Per Mertesacker to start his first game in 392 days.
Aaron Ramsey's late goal earned Arsenal their thirteenth FA Cup triumph at Wembley.
"I expect myself to perform at that level every single week", Mertesacker said.
"I feel I know I am in a public job, I accept to be criticised and I accept people don't agree me".