The hosts managed a late consolation goal from Zander Diamond deep into stoppage time after Pompey had been reduced to 10 men, but it was too little, too late.
Burton boss Rowett said: "We've not done enough to win the game. At home, we've not played with anything close to the intensity and brightness we showed last season.
"We knew that would be difficult to replicate because we had such a terrific home record and we have been better in away games so far.
"We're not getting the rub of the green either because I cannot for the life of me understand how a foul was not given in the build-up to their second goal. It was so blatant to me.
"It was a very poor decision that made the game even more difficult for us to win. But at the same time we have slipped into a little period where are not doing enough to win games and we have to work harder to create chances."