Arsene Wenger's charges were able to grab two crucial goals on the road at San Siro courtesy of Henrikh Mkhitaryan and Aaron Ramsey, leading Bonucci to highlight his team's fear during the first leg of the contest.
"A little fear and anxiety set in during the first half. It'll all help players to gain experience," the Milan skipper told Sky Sport Italia.
"The second leg will be difficult to turn this around, but anything can happen in football. We can't get away with failing to defend and attack as a team. We couldn't get the shape right and Arsenal moved the ball quickly to stretch us too.
"If we go to London with the spirit we showed in the second half, then we can get a result. I think today we lacked the courage to take on responsibility, both in possession and closing down their passing channels. We did better after the break, but allowed Danny Welbeck that one chance on our error. We could've done a lot better with our passing and control."
Bonucci's Milan now take on Genoa in Serie A at the weekend, before trying to bounce back against Arsenal at the Emirates in the second leg next week.