Aaron Ramsey scored an extra-time winner at Wembley to defeat Hull City 3-2 and seal Arsenal's first trophy in nine years.
But Adams feels there is still work to be done, and claims the forthcoming transfer window could be pivotal for manager Arsene Wenger.
"I believe football clubs are about balance and I don't think he's got the balance right," he told Sky Sports News Radio.
"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."
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