Roy Hodgson's side made it three wins from three in Group E of Euro 2016 qualifying on Sunday with a hard-fought 1-0 victory over Estonia in Tallinn.
England needed Wayne Rooney's late free-kick to secure maximum points after struggling to break a resolute Estonian backline.
Wilshere, who formed part of a midfield trio alongside Jordan Henderson and Fabian Delph, was pleased with the resilience he and his team-mates displayed and feels England are becoming a tougher unit.
"We're trying to become better as a team. On the pitch and off the pitch we are really close - on the pitch we are starting to become a horrible team to play against," he said.
"We've got a great, compact unit there in the middle, we get after the ball and we win it. We talk about the 'five-second fury', when we lose it - go get it back. We are starting to do those things.
"In the first half we should have scored a few goals but in the second half we felt confident.
"Even when they went down to 10 men it might have made it a little bit harder, but we kept going and Wayne produced a bit of magic."
