The Gunners suffered a surprise 1-0 loss to the Swans at home in the Premier League on Monday.
Bafetimbi Gomis’s headed effort in the 85th minute proved to be the difference between the two sides at the Emirates Stadium in North London.
Next up for Arsenal is a clash against Manchester United away from home at Old Trafford on Sunday, and Wilshere is confident that the Gunners will pick up all three points.
“We’ve been there in the FA Cup this season and won, so we know what it takes,” the England international told Arsenal’s official website. “Our confidence will be high going there but we’ve got to perform.
“It’s no good just going there thinking that we can beat them again because we’ve beaten them before. We’ve got to put in a performance, work hard and earn the right to win.”
Arsenal will head into the encounter at Old Trafford placed third in the Premier League table with 70 points from 35 matches.
The Gunners are currently three points behind last season’s champions and second-placed Manchester City and two ahead of Manchester United, who are fourth in the standings at the moment.
The advantage that Arsenal have over both City and United is that they have a game in hand, which makes them the favourites to finish second in the table behind champions Chelsea.
The top three teams in the Premier League automatically qualify for the group stage of the 2015-16 Champions League campaign, while the side which finish fourth will have to go through a playoff round.
Sunday’s match between United and Arsenal could prove to be decisive in that regard.