The England international has told his team-mates to keep pushing ahead of upcoming games against West Ham and Tottenham, and their Champions League second leg with Bayern Munich
The Gunners are on the brink of another trophyless season after falling behind the two Manchester clubs in the race for the title and losing out in both domestic cups to lower league opposition.
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Despite looking set to miss out on silverware for an eighth successive season, Wilshere is hoping that they can fight for third place and potentially save their Champions League dream.
Arsenal face Tottenham in the north London derby next weekend, and Wilshere is urging his team-mates to up their game.
"Our season is definitely not over,” the 21-year-old midfielder told The Sun.
"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."
The Gunners beat Aston Villa 2-1 on Saturday, a result Wilshere feels will have lifted some of the pressure off manager Arsene Wenger, who has come under criticism in recent weeks.
"It was a massive win, especially after the midweek disappointment," Wilshere 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]."