Before the game at Glanford Park, Vale had beaten both Sheffield United and Wednesday in the previous rounds and that is something of note according to the boss.
Adams said: "I think we can be proud of what we have done, with a bit of luck, it might have gone our way.
"We had chances in the first half and we had chances in extra time after they scored. Their keeper played really well in extra time. It just wasn't our night."
"It's all important now, we've got to take a great deal of confidence from this run and push on in the league now," he added.