Rovers were made to work hard throughout against a tough Lions side in tricky conditions, eventually running out 3-2 winners.
"We're delighted that we've won the game, but we've played a lot better than that and lost," Bowyer told Radio Rovers after the game.
"So I'm happy that we've fought it out and ground it out and got the three points but in terms of the performance it is probably one of our worst of the season.
"I'm delighted with the character that they showed, they stayed in it because it was a tough battle.
"You are due some of them over the course of the season and that is our first one. We've played loads better throughout the season and lost a couple of games so it was important that we got the three points."
Rovers opened the scoring in style with Jordan Rhodes grabbing his 12th goal of the season, but MIllwall levelled through Martyn Waghorn.
Ben Marshall's first goal for the club restored Rovers lead, which was then extended by David Dunn's close-range header.
But to their credit Millwall made it 3-2 a minute from time through Morison to set up a nervy ending.
"I thought we scored two very good goals," added the manager. "Jordan's first one is outstanding, an outstanding finish.
"Then we'd worked on getting balls into the box and Tommy Spurr produces a fantastic cross and I'm delighted for Marshy because I thought he did very well.
"You then bring Dunny on for his experience and he pops up with a goal. So with the quality of our goals we are delighted, but our passing today wasn't great.
"To concede at the death made it tense and you knew what Millwall were going to do in chucking the ball into the box.
"We've seen the character and the resilience come through because we've had to fight for everything today.
"It was a horrible day, the conditions weren't great and the game wasn't great but they stuck at it and so did the supporters."