Saturday's penalty shootout win over Wigan Athletic at Wembley edged Wenger's men a step closer to a first trophy since 2005 as they booked a place in the final, but Tuesday sees them switch their focus back to the league and the quest for a top-four finish.
In the title race for much of the season, Arsenal have dropped well off the pace in recent weeks, and currently lie in fifth spot, 13 points behind leaders Liverpool.
With five matches remaining, Arsenal are two points behind Everton, although on paper their run-in looks kinder than that of Roberto Martinez's side, who have games against both Manchester United and Manchester City to come.
But as he turns his attention back to the league, Wenger is hoping to build on the momentum of their cup run.
"I think if we win our games we will finish in front (of Everton)," he told the club's official website. "For us it's important now to focus on the Premier League and if we do that well I'm confident we will come back.
"We have a final in the FA Cup but we now have a period where we can concentrate on the Premier League."
Tuesday sees them come up against a West Ham side with seemingly little to play for, but midfielder Mark Noble wants a strong end to the season to equal last year's 10th-placed finish.
West Ham were second from bottom after a 2-1 defeat at Fulham on New Year's Day, three points from safety, but a run of four consecutive wins in February saw Sam Allardyce's men pull away from danger.
They currently sit 11th, six points adrift of the top-half finish they crave, and were victorious last time out on the road, Andy Carroll and Mohamed Diame scoring in a 2-1 win at Sunderland.
"Our aim since the start of the season has been to at least match last year's finish," Noble told the club's official website.
"We didn't have the best of starts, we know that, but since Christmas we've really dug in and put the points on the board.
"There's five games left that we need to get points from and come 10th again."
The hosts will be without the suspended Mathieu Flamini, while the likes of Mesut Ozil (hamstring) and Laurent Koscielny (calf) remain doubtful.
For West Ham, defensive trio James Collins (calf), George McCartney (hamstring) and Joey O'Brien (shoulder) are all injury concerns for Allardyce.
