Wenger has won the competition on four occasions but not since 2005, when Arsenal beat Manchester United on penalties at the Millennium Stadium in Cardiff. That is the most recent trophy in Arsenal's cabinet, though the club reached the 2006 Champions League final and two subsequent League Cup finals.
Arsenal have secured Champions League qualification for 15 successive years but the pressure on Wenger has been ratcheted up to a new level as a large number of supporters have become increasingly frustrated with the shortage of silverware.
The manager says he shares those frustrations. "It bothers me, of course it bothers me, because I'm not here to watch other people win trophies," said the Frenchman. "It is important and I will give my best to win on Sunday. I will just remind you that I have won the FA Cup four times."
Asked about the incessant talk of eight years without a major title, Wenger added: "Of course that's not pleasant, but the only way to [end] it is to win."
Swansea have got the better of Arsenal since their return to the top flight. Last year, under Brendan Rodgers, they were beaten 1-0 in the Premier League at the Emirates Stadium but came from behind for a 3-2 victory at the Liberty Stadium, while earlier this season Michu scored twice to secure a 2-0 victory for the Welsh club in north London, in what was arguably the nadir of the league campaign so far for Wenger.
That was Arsenal's last defeat in the league and Wenger hopes his side will hit back with a win: "They had a very good game here. We have to give them a different response on Sunday."
Asked if victory would take the pressure off securing silverware, Wenger added: "You cannot speak about winning a trophy. For us it's important to show continuity and consistency and the FA Cup is part of that. To get people to believe more in the team it's important that we win on Sunday."
Arsenal have allowed Marouane Chamakh to join West Ham on loan until the end of the season as the Moroccan forward has failed to make a single league appearance this season. Chamakh did play in the penalties defeat to Bradford City last month, when Arsenal went out of the Capital One Cup to the League Two side.
Wenger, though, is keen to consign that loss to the history books with safe passage on Sunday. He said: "I think it is an important moment of the season for us, for the team to strengthen the confidence of the team. We feel we are on a good run but how far can we go, to win in the FA Cup will strengthen. It's an important moment of the season."
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