Saturday's penalty shootout win over Wigan 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.
With five matches remaining, Arsenal is two points behind Everton, although on paper its stretch run looks kinder than that of Roberto Martinez's side, which has games against 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 the 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 the Gunners 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-place finish.
West Ham was second from the 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, with 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, the defensive trio of James Collins (calf), George McCartney (hamstring) and Joey O'Brien (shoulder) are all injury concerns.