The club's first visit to the Keepmoat Stadium ended in a first defeat as a dubious Theo Robinson header and a fortunate James Husband cross saw the home side claim all three points.
"First and foremost we are disappointed that we are going away from here empty handed," said Bowyer after the game. "It is not acceptable from us to accept the result.
''I thought we came and were dominant in possession but unfortunately we've gone in at half-time 1-0 down off the back of two refereeing or linesman's decisions.
"Their lad is offside for the first one when he heads it in the goal, we've seen that again. Then we have a goal disallowed against Chris Taylor when quite clearly, and it is clearly, that Jordan Rhodes is onside at the beginning.
"Then Jordan Rhodes goes around the goalkeeper and just misses in the first half.
"The way that we passed the ball around was pleasing and we continued in the second half in the same vein but we get done by what can only be described as a fluke so that is majorly disappointing.
"Everybody in there is desperate to win and unfortunately tonight we've not been able to do that. They are professional people in there and they are disappointed.
"The three games we have played we have lost two and it isn't through the opposition dominating us, it has been by flukes."