The North Londoners recovered from two early goals to pip Hull City to the FA Cup title at Wembley on Saturday to end a nine-year wait for a trophy.
Questions have since been raised whether or not Wenger's side can use the triumph as a platform for which greater success can be built, but Adams feels that the Frenchman must recruit more defense-minded players to help Arsenal win further honours.
Adams, who has a statue commemorated to him outside the Emirates Stadium, told Sky Sports Radio: "I believe football clubs are about balance and I don't think he's got the balance right.
"He's got too many offensive players. Ozil was a fantastic signing and he's a super player, but let's have some more at Arsenal and some more trophies. I do think that we've got a lot of those players - Cazorla, Wilshire, Ramsey and Rosicky has had a super season.
"I'd like to see two strong full-backs and maybe one more strong midfield player - Manu Petit or Patrick Vieira back in the day - someone to just sit in there and be a bit different."
The 47-year-old won three FA Cup titles - two under Wenger - in his 19-year stint in North London.