Ravel Morrison fired the hosts into a 42nd minute lead, while Jordan Rhodes levelled matters at St Andrews on 66 minutes.
And Rovers' caretaker boss Bowyer said: "We were poor in the first half as we didn't play to the tempo and intensity as we have done over the last couple of weeks.
"I thought it was very much end of season but, in the second half, we deserved a goal and in the end we might have nicked the game."
Bowyer, who is now waiting to discover his future at Blackburn, praised his team's goalscorer Rhodes.
He said: "It was a great finish from him being in the right place at the right time.
"He has been outstanding for us all season. Rightly so he has got all the plaudits."