Veteran striker Lee Hughes struck twice from the penalty spot after opening the hosts' account with a firm header, with his hat-trick contributing to Vale's biggest win in 53 years in front of 10,978 supporters on Friday night.
Ben Williamson also grabbed a brace for second-placed Vale while Tom Pope, with his 32nd goal of the season, and Chris Birchall were on target as well, substitute Matt Paterson netting Burton's impressive consolation.
The emphatic defeat leaves fifth-placed Albion winless in four games with just a further four remaining this season in League Two.
Rowett admitted: "They were a lot better than us. They were strong and ran with more desire.
"But that's 10 goals we've conceded in two games and we can't keep defending like that. It's given our goal difference a massive battering. So we've got to put it right.
"I always thought our two home games coming up against Wycombe and Plymouth would define our season more than this game.
"But for 20 minutes in the first half we were all over the shop and we made poor decisions on the ball. We gave ourselves a mountain to climb.
"Matt Paterson came on and showed some real desire and his finish was sensational and it was just unfortunate the game wasn't tighter.
"It's a test for everyone now as we have been on a poor run."