The north London outfit have endured a torrid couple of months as they have won just two of their past seven Premier League games, leaving them languishing in eighth place.
This poor Premier League form was exacerbated with a disappointing Capital One Cup performance that led to them being knocked out by Bradford on penalties.
Despite these setbacks, the English international remains confident that his team can compete for honours this season,
"We can still realistically win everything we are in. I know we are a long way behind in the Premier League but football changes quickly," he told Sky Sports.
"If we win three games and another team loses a couple and draws one, we are back in it. It is not in our hands so we need a bit of luck."
Wilshere also spoke of potential Champions League glory, admitting that it was going to be difficult but, citing Chelsea's heroics last season as a point of comparison, emphasised that anything is possible.
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"You saw with Chelsea last year, no-one would have said in December they were going to win the Champions League. But they got a bit of luck. There are top-quality teams and the best players in Europe so you are going to need a bit of luck."
With Arsene Wenger coming under increasing pressure, Wilshere was also keen to defend his manager, hailing his legacy and laying the blame on the players rather than the coach.
"He has built a legacy at this club. He changed everything from when he came in 15-16 years ago. He brought the Total Football, if you like, to Arsenal - the passing game," he continued.
"For me, there is no question he is the right man. You cannot start questioning him because we have had a few bad results. The players have to look at themselves."