Adams, who returned to the dugout for the first time following a three-game absence due to hip surgery, believes that the decisive goal could have been avoided.
He told reporters: "It is gutting. I think the game plan was spot on. The effort, enthusiasm, all the things that we probably lacked against Rochdale on Tuesday was there.
"We won tackles and closed people down. You could be slightly critical of what we did when we went forward but we were playing against a very good team.
"To lose to a goal at the death like that, which I think could easily have been avoided, is very disappointing.
Port Vale, who remain 12th in League One, travel to Sheffield United next Saturday.