Clashes between England and Russia fans around Saturday's 1-1 draw in Group B prompted UEFA to warn both sides that they could be kicked out of the tournament if the scenes were repeated.
Wilshere was brought on as a second half substitute at the Stade Velodrome and admitted the England players were aware of the unrest before and during the match.
But he rebuffed suggestions the supporters had let their team down, saying: "Of course not. I wouldn't say that. Their support in the stadium was fantastic and it always is – it was the same in Brazil.
"There was obviously a little bit of trouble but from what I saw in the stadium the fans were brilliant and we thank them for that.
"Before the game we were obviously aware because every single player has got a Twitter account and you can see over that. But as soon as we got to the stadium we felt the fans, it was fantastic support in the stadium."
Wilshere added the threat of expulsion would not affect the team.
"We let the people in the right positions deal with that kind of thing and we just need to concentrate on football," he continued.
"The fans in the stadium were brilliant. They helped us to perform the way we did. The trouble in the game you are not aware of while you are playing – it is only after the game you are made aware of it."
After missing most of the 2015-16 season with a leg fracture, Wilshere is feeling the benefit of three appearances for Arsenal and a pair of starts in England's warm-up fixtures for Euro 2016.
He is hopeful of breaking into Roy Hodgson's starting line-up for the next Group B match against Wales.
"I feel good and sharp. I have been back a while now and got a good number of games under my belt. I was delighted to get on [against Russia]," Wilshere said.
"Every single player in the 23 wants to play. If you can't get in the starting 11 you want to get on and help the team."