Arsenal supporters vented their frustration at Wenger following the loss to Villa, pointing at the lack of activity in the transfer market.
But the Frenchman, boss since October 1996, will not be rushed as Arsenal bid to secure their Champions League group place on Tuesday night in the return leg with the Turkish side at the Emirates Stadium.
"We are a bit short numbers-wise for the whole season, to go for all the competitions," Wenger said.
"We have at the moment injured players, like (Alex Oxlade) Chamberlain, like (Mikel) Arteta.
"But we have as well not to panic and to make the right decision. `Under pressure, that's never easy. But we will do it."
Although recognising he must add to his squad, Wenger also has faith in his existing group of players, which features a young core of British talent.
"During the transfer period people are so focused on who is coming in they forget how good our players are," he said.
"If you look at our team (against Fulham) you had (Carl) Jenkinson gets the chance to start, (Theo) Walcott, (Aaron) Ramsey, (Jack) Wilshere, (Kieran) Gibbs.
"You (the media) should give us some credit for that sometimes."
The goals came from Olivier Giroud, with his third of the season, and Lukas Podolski, who scored twice, but another crucial intervention was a double save from Wojciech Szczesny, who has been the subject of scrutiny in recent seasons.
"You have to trust your players," Wenger said. "The goalkeeper is 23 years old. It's his third season now in the Premier League. He's growing now.
"The young players you have to trust to give them confidence."
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