The Cottagers held firm until the 57th minute but two quickfire goals from Santi Cazorla secured a 2-0 victory that kept Arsenal top of the Premier League table.
"We've had a few games like that here this season where teams have come here and tried to stop us from playing but we've shown once again we can break anyone down by being patient," said Wilshere.
"We know we are going to create chances and Santi came up with the goods today.
"We're still top of the league and that gives us good confidence and we'll look forward now.
"We know we are going to be able to score goals, it's just a matter of putting the ball in the net and being tight at the back, which we've done this season so hopefully we can continue."