The Gunners look likely to finish the season without a trophy, having been knocked out of the FA Cup to Blackburn Rovers last weekend before losing 3-1 to Bayern Munich in the Champions League a few days later.
However, the North London outfit picked up a 2-1 win over Aston Villa on Saturday, and Wilshere admits that the victory was massive for his side.
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.
"It was a massive win [against Villa], especially after the midweek disappointment. 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]."
Arsenal travel to White Hart Lane to face rivals Tottenham Hotspur on Sunday.