"We needed to show some character, and some resilience, and as well some nerves, and we did it in a very united and resilient way.''
Victory took Wenger's team into their first FA Cup final since 2005, when they last won a trophy, and helped ease the pain of being knocked out of the Premier League's top four by Everton earlier in the day.
They will play the winners of Sunday's second semi-final between Hull City and third-tier Sheffield United.
Uwe Rosler's Wigan, meanwhile, must turn their attentions back to the Championship promotion chase, having been thwarted in their attempt to become only the seventh club to retain the FA Cup.
"I couldn't ask for any more than what they've given me,'' said Rosler, whose side eliminated his old club Manchester City in the last eight.
"Arsenal are one of the top teams in the country and we did very well. I'm absolutely proud of how they played and what they put in.''
The game was preceded by a minute's silence in memory of the 96 Liverpool fans killed in the Hillsborough disaster, which occurred during an FA Cup semi-final in Sheffield on April 15, 1989.
Ninety-six seats were also left empty on the halfway line.
-AAP