Wilshere, who came on as a substitute with 20 minutes to go, just before Blackburn scored, cut a forlorn figure at the final whistle as the Gunners crashed out on the back of a 1-0 loss at the Emirates.
The England international, though, maintains the squad have no option but to pick themselves up and raise themselves for another stern character test when they will face German powerhouses Bayern Munich in the first leg of their round-of-16 clash at home on Tuesday.
"We know what this trophy means in England and we wanted to go all the way, but now we have got to regroup," he said.
"We have got a big game on Tuesday and we need everyone behind us.
"We have beaten big European teams here before so we need to do that again."
Wilshere feels Arsenal can draw on the progress made by Chelsea last year, despite their inconsistent Premier League displays.
"Chelsea weren't having a good season and they got a bit lucky in some games, but showed great character. We need to do that now and come together as a team," he added.
The Blues finished fifth in England last season but upset all the odds in the Champions League, beating both Barcelona and Bayern Munich to win the continental trophy for the first time in their history.