First-half goals from Jordan Rhodes and Scott Dann were enough to give Rovers their first win in 10 league games and end a run of two successive defeats.
Rhodes converted an early penalty and Dann headed in his fourth league goal of the season to inflict a second consecutive defeat on the Rams.
"The situation that we're in now, if we're fourth from bottom on May 4, there will be a lot of happy people," Bowyer said.
"Not for the reasons we should be happy, but because we've stayed in this division.
"We can't look any further than Tuesday [when Huddersfield visit Ewood Park]. As much as we want to enjoy this win, we've got to refocus on preparing properly.
"I thought the energy we showed and the way they went about it was pleasing. We started the game on the front foot and got the penalty that settled us down and gave us confidence. It gave us a boost. Obviously to score right on half-time was excellent timing."
- Sports & Recreation
- Scott Dann
- Jordan Rhodes