Goals from Fraizer Campbell, Joe Mason and a Peter Whittingham penalty secured three valuable points for the Bluebirds who have a seven-point lead at the top of the table and they look to be heading to the Premier League.
Rovers were relegated from the top flight last season and their latest defeat leaves them in 19th place - just two points off the bottom three.
And Bowyer admits the prospect of a second consecutive relegation is not a happy one.
"The club were relegated from the Premier League last season so we know what it feels like. We don't want it to happen again this time," he said.
"My overriding emotion is one of disappointment. We withstood an enormous amount of pressure in the first half, but I thought the first goal was a foul on the goalkeeper.
"We are not getting those decisions at the moment."