"I'm especially proud of the way we won this season, in the semi-final we had to play against Man City here and in the final Chelsea here, you can not get tougher and we had two outstanding performances, this cup was won with special spirit and special attitude".
Gilt-edged chances for Mesut Ozil, Danny Welbeck and Aaron Ramsey followed Sanchez's opener as Arsenal looked to move out of sight before the interval, but Chelsea held firm to gain a foothold in the game after the restart.
Just as the season reached its climax, Arsenal turned in the type of tenacious display lacking so often, and against a side so commanding in the Premier League in Antonio Conte's first season in charge.
He was all smiles though as he joined the ecstatic celebrations on the Wembley pitch where Aaron Ramsey's late header ensured Arsenal have now won three of the last four FA Cups after an interminable 10-year trophy drought. "Wednesday or Thursday will be clearer".
"I'm happy for the manager", Ramsey said. "Hopefully, he'll be there next season".
For once, this was a day when so much went right for Wenger, even with a patched-up injury-depleted defense featuring captain Per Mertesacker making his first start in more than a year.
"We had an outstanding performance from the first minute onwards. Overall, we'll know more next week".
But the season has ended with a run of six victories in May after Wenger adopted the three-man defense that has served Conte so well, until now. They showed strength and unity and played spectacular football today. The linesman had flagged for offside but referee Taylor overruled his assistant after a 30-second deliberation, and awarded the goal.
In the second period, the Blues improve, but were dealt a major blow on 68 minutes when Victor Moses was rightly sent off after picking up a second yellow for an obvious dive.
"You always worry when Chelsea got the equaliser and it was a game full of surprises".
Defeat blew Chelsea's chance of the double, although there is still plenty to celebrate in west London after a memorable season for both the club and Costa.
When asked whether he believed he had the backing of the board he confessed: "I can't answer that", said Wenger. "He put it on a plate for me to score the victor".