Cardiff were never in danger of losing this one after Fraizer Campbell gave the Welsh outfit the lead.
Further goals from Joe Mason and Peter Whittingham made sure of the points putting Cardiff another step closer to the Premier League while Rovers are left to stare relegation in the face.
After suffering relegation from the top flight last season, they now sit in 19th place with a cushion of just two points between themselves and the drop zone.
Bowyer told Sky Sports: "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.
"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."