Leon Best's late equaliser salvaged a point for Rovers in their season opener, but Bowyer is adamant that his team could have taken all three.
"We should have got three points," the club's official website quotes him as saying. "We were that good today.
"I thought we started very very well but unfortunately the injury to Rochina just rocked us a little bit.
"But overall if you look at what we've done, we've hit the bar, we've hit the post, we've had chances cleared off the line and we've played the better football against a team that only lost three at home all last season in the Championship."
Derby led since shortly before half time courtesy of a Johnny Russell penalty, but Best levelled with little more than two minutes left on the clock.