The Gunners fought back from a goal down to take a 2-1 lead against Manchester City at the Emirates Stadium on Saturday, but could not hold out for the three points.
"Towards the end of last season when it looked like we weren't going to get in the top four we said, 'listen, this is not good enough'," Wilshere told the club's official website.
"But since the last seven or eight games of last season to now we've had a fantastic attitude. Everyone in training is buying into the defensive side of the game - we want to improve that, winning the ball back high up. Our quality is on show."
The Gunners face Borussia Dortmund in their first Champions League match of the season on Tuesday.