The Gunners beat a 10-man Chelsea squad, 2-1, thanks to a controversial Alexis Sanchez goal in the opening minutes and a late victor from Aaron Ramsey in response to the Blues' lone score of the match.
Wenger, who failed to finish in the top four in the Premier League for the first time since taking charge in 1996, celebrated with his players in front of the massed red ranks of Arsenal fans at the end.
Wenger has now won the FA Cup a record seven times, but uncertainty hangs over the 67-year-old heading into the close-season.
"He has been calm and quiet as he has always been when dealing with those situations", the German said.
Arsenal's Aaron Ramsey was ruled offside but Antony Taylor overruled his assistant's decision and allowed Sanchez's goal. On Saturday he drafted in Per Mertesacker, his captain who had played only 37 minutes of first team football all season because of injury.
Arsenal were rampant in the first-half against a Chelsea side who looked well off the pace, with Danny Welback and Ramsey hitting the woodwork and Mesut Ozil failing to make the most of a great chance. We don't know how the decision will go.
'We are at the end of the season and a lot of players are exhausted and then there is a lot of pressure'.
"I think obviously when he went inside there was a moment when I sort of went to go for the ball, and then I thought he might just be a little bit ahead of me so I chose to pull out and not go for it".
All our players should be fit and raring to go from the start of the campaign, and with all our rivals facing tougher opponents in Europe than we will face, perhaps next year really could be our year?
"Maybe now we're a bit sad, but we shouldn't forget the awesome season we've had being (Premier League) champions", Courtois said.
"I'm very proud, if nobody has done it since 18-god knows-when it means it is not easy".
Asked if delivering the FA Cup would be a ideal way to say goodbye having been at the club almost 21 years, Wenger replied: "There is no flawless way".