The Gunners slipped to an agonising 2-1 reversal against German opposition on Tuesday, with Robert Lewandowski grabbing a dramatic winner eight minutes from time.
Arsenal had been pushing for a clincher of their own when Dortmund struck on the counter, but Wilshere insists heads will not be dropping at Emirates Stadium after a first defeat in 13.
He told Sky Sports: "They are a good team. They came here and they showed that.
"They moved the ball around well, they are difficult to break down, but we had our chances - Santi (Cazorla) hit the bar and we had a few more. They hit us on the break and they nicked a goal, but it was a good goal and we'll bounce back."
Asked for his take on a group which now includes three sides on six points, Wilshere added: "Very tight, very interesting. Napoli won tonight, which makes it even more interesting.
"We're all on six heading into the last three games, so it's all to play for and we know what we have to do now."
Wilshere was replaced just before the hour mark against Dortmund but, despite requiring treatment on a troublesome ankle during the first half, the England international insists he has suffered no long-term damage.
He said: "I'm alright. I just jarred my ankle.
"I have done it before and it's painful for the first minutes or so, then you can run it off and I'm alright at the minute."