Following a goalless period of extra time, Arsenal went on to win the semi-final on penalties against the Championship side.
"The win will rebuild the confidence which was very jaded, I'm confident we will respond well," Wenger is quoted as saying by talkSPORT. "We were under a lot of pressure to win today. We needed to be resilient against a really strong Wigan side.
"My emotions were going through the roof and unfortunately that takes a few days off your life. I suffered less during the penalties than during the game, but when it finishes well you don't mind too much. We did it and we were calm in the shoot-out which was fantastic.
"It will give us a target for the end of the season and it allows us to focus on the Premier League in a more serene way. We had the nerve and the mental strength that has been questioned recently, that's why I'm happy they gave that response. I was never worried about that, but you have to show it in the great occasion."
Arsenal will face either Sheffield United or Hull City in next month's final, with the pair meeting tomorrow.