The visitors created a host a chances at the Amex Stadium but were undone by an Ashley Barnes double, either side of a goal from young midfielder Jake Forster-Caskey.
Defender Tommy Spurr headed against the crossbar and Jordan Rhodes and Dickson Etuhu should have both hit the target.
Bowyer said: "We are very disappointed to leave without anything, but we found their keeper inspired. He was the man of the match.
"Unfortunately, we gave three goals away and must cut out individual errors. They are very costly at this level.
"Had Jordan scored just before half-time it might have been a different game."
Rovers have only won once away from home and Bowyer admits this is a "concern".
He added: "Our home form is good but we must stop coming away and giving sides a head start."
For the second successive time, Rovers have gone into an international break on the back of a defeat but Bowyer insisted: "The scoreline flattered Brighton.
"We are really, really disappointed not to get anything, especially as we created even more chances than when we won at Bournemouth."