The Gunners' trophyless run could stretch to eight seasons this year, having failed to establish themselves in the Premier League title race and with their UEFA Champions League campaign on the brink.
Arsene Wenger's men crashed out of the FA Cup last weekend before suffering a 3-1 defeat in the first leg of their last 16 tie at home to Bayern Munich in Europe in midweek to give themselves a mountain to climb on their visit to Germany next month.
But they narrowly beat Aston Villa on Saturday to give their hopes of a top-four league finish a boost and Wilshere insists they still have much to play for.
Ahead of next weekend's clash with local rivals Tottenham, Wilshere told The Sun: "Our season is definitely not over.
"We've got a big chance against Tottenham. We've got another big game at Bayern.
"It will be tough but if we show no fear, anything can happen."
Wenger has come under increasing pressure in recent weeks as Arsenal's hopes of silverware have faded and Wilshere was glad the players could ease some of the heat on the manager on Saturday.
"It was a massive win, especially after the midweek disappointment," he added.
"We take the pressure. I think the manager takes it as well. He stands up for us the whole time. But we as players have to take the pressure on and relieve the pressure like we did (on Saturday)."