First-half goals from Louis Dodds and skipper Doug Loft put Vale on their way and striker Ben Williamson capped a one-sided affair with his side's third goal 12 minutes after the break.
Barker admitted it was an uphill battle following Dodds' early goal, which came about from an error by defender Joe Walsh.
He said: "Walsh's mistake set the tone for the rest of the evening.
"Just as last Saturday's win over Bradford was our best performance, so this display was probably our worst.
"The first goal changed the game and gave Port Vale confidence. They were very organised."
Nevertheless Barker is proud of his team's record of having lost only five of their last 28 league games since the middle of last season, and called the defeat a "slight blip."
He added: "There's been no ranting and raving in the dressing room, we will just work on the problem. One defeat in the last eight is as good as we could have asked for.
"Port Vale made four changes; I don't think if I could do that as we don't have the resources. This result brings everybody down to earth after last Saturday and shows that there is not a team who will roll over and die."