The Gunners ended a nine-year trophy drought last season, beating Hull City in the FA Cup final, and had hoped to kick on, but Campbell doubts Wenger's side can go on to win domestic league or European honours this season.
"I don't know if the FA Cup is taken as seriously as it was when I played but it should be treated seriously because it offers Arsenal the best chance of some silverware this season," Campbell told the London Evening Standard.
"Arsenal aren't going to win the Premier League this season and although Monaco is a very winnable tie in the Champions League there are some big teams in there even if they do get through - so you have to say Arsenal should be competing to win the FA Cup again.
"I said before the Wigan game [last season's FA Cup semi] they have to treat them with respect and do everything right - and the same applies to Brighton away."
For the big stories and the banter follow us on Twitter: @tribalfootball