The Frenchman has defended his side after a week in which they all but exited European competition with a 4-0 first-leg loss to AC Milan and were knocked out of the FA Cup by Sunderland.
Barring a miracle in the second leg at the Emirates against Milan, Arsenal are heading towards a seventh successive season without a trophy.
However, Wenger believes that simply attaining Champions League qualification should be viewed as a huge achievement.
"The first trophy is to finish in the top four," he told reporters after the defeat to Sunderland. "And that's still possible. I believe finishing fourth is vital for us, so let's focus on that.
"That we lost here is basically down to the fact that we had to give a lot in Milan on Wednesday night and then we had to travel again, and that is difficult for any team in the world. But I thought it was a good performance from us."
Arsenal's next game is the north London derby against Tottenham, a side who have been in fine form this season, but Wenger is still confident about getting a good result.
He added: "We put a lot of spirit into playing Sunderland and if we keep that spirit and recover a little bit physically then we can win the next game."
The 62-year-old also hinted that he is not reluctant to delve into the transfer market but bemoaned the injuries his side had suffered.
"When everybody is available we have what it takes at the club and we will add what it takes. But at the moment we're not making plans for next season, we're making plans for the next game.
"We have many missing: big, big players too. We're in February and [Jack] Wilshere has played zero games; [Abou] Diaby has played zero games [Per] Mertesacker is out for the season and [Andre] Santos for three months.
"That would be difficult for any club in the world to deal with. But let's win our next game and we'll be fine."
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