Szczesny insists ambitions are higher merely than a Barclays Premier League top four finish.
He said: "We are outside the top four so our first target is to reach that top four. But our ambitions are much higher than that.
"We have managed to get a couple of good results recently. We need to climb the table and hopefully do well in the other competitions as well.
"I think in the last two matches before Villa - against Tottenham and Montpellier - offensively we played really well.
"We had a few disappointing performances before that, so it's important we get back to that level and I think we are in a good position to do so."