Aaron Ramsey scored an extra-time winner as Arsenal came from two goals down to triumph 3-2 over Hull City at Wembley, sealing the club's first trophy for nine years.
And Wenger believes Saturday's victory could be the beginning of another successful era for Arsenal.
"We wanted to make history tonight and win the game," he told ITV. "And we made history both ways - how not to start a cup final and how to come back.
"I'm very happy for the players because I think it was a turning point in the lifespan of this team.
"To know that they can win in that way was very important today.
"We came back, and I have praised many times the spirit of this team and I'm very proud of that today."
James Chester and Curtis Davies found the net to put Hull 2-0 up inside eight minutes, but goals from Santi Cazorla and Laurent Koscielny forced the game to extra time, with Ramsey settling the tie in the second additional period.
And Wenger, who appeared to indicate that he would now sign a new deal with the club, spared a thought for runners-up Hull.
"Congratulations to Hull, they played fantastic for the whole game," he added. "We won it in the end, but they played very well.
