The midfielder has also spoken out about Danny Welbeck’s controversial penalty incident.
Arsenal beat AC Milan 3-1 (5-1 on aggregate) to progress to the quarter-finals of the Europa League.
Because the Gunners are 12 points outside of the Champions League places in the Premier League table, their best hope of qualifying for the tournament next year is by winning the Europa League.
And Wilshere was delighted that his side made it through to the last eight.
“We needed it,” he told BT Sport.
“We set the level last week in Milan. It was about getting the job done tonight and being professional. We didn’t start well but it woke us up.
“They got a good goal early on and made us work for it. We are happy to be through to the next round and we will see who we get.
“I hope so. When we looked at the draw before, AC Milan was probably not one of the teams we fancied but we showed we can play against the top teams in Europe.”
Arsenal beat Milan thanks to a Danny Welbeck brace either side of a Granit Xhaka strike.
But it was the England international’s first goal which was shroud in controversy as he went down easily when goalkeeper Gianluigi Donnarumma came rushing out to close him down and won his side a penalty.
And Wilshere claimed to not see the incident, a remark which was echoed by many of his team-mates.
“I haven’t seen it,” he added.
“The defender was between him and me. I will ask him afterwards.”