The Gunners had led 2-0 at the Emirates only for Spurs to win 3-2 but they had enough to claim all three points at Villa Park and go top of the Barclays Premier League.
Wilshere told Sky Sports 2: "I think there's always going to be that (uncertainty) especially after last week.
"It was a good ball from Chamakh and I'm happy to get my first goal."
Wilshere praised the way his team-mates had applied themselves this season.
He said: "I think it's down to hard work."