The Gunners slumped to a fourth consecutive loss across all competitions at the Amex Stadium - their worst run of form for 16 years and a result which leaves them 13 points adrift of the top four.
Calls for long-serving manager Arsene Wenger to step down were once again heard during the defeat, but Wilshere urged the supporters to stay with the club.
I'm sorry to the gooners out there. You deserve better. Thats all i have to say. I know its difficult at the moment in this difficult period we are going through as a team but we need you. We will do better but please stick with us ❤ pic.twitter.com/UTsCdXkQmB— Jack Wilshere (@JackWilshere) March 5, 2018
Arsenal must now turn their attention back to the Europa League, where they will face AC Milan in the first leg of their last-16 tie on Thursday night.