A first half header from Fraizer Campbell was added to by strikes from substitutes Joe Mason and Peter Whittingham to give the home side a comfortable afternoon.
It was Bowyer's first defeat as Rovers boss and it was a feeling he doesn't want to repeat.
"It doesn't feel very nice, I don't like the feeling," said Bowyer of the loss. "The players didn't like the feeling in the dressing room afterwards.
"The standard of our first half play was not at the level that they can perform.
"We came under a lot of pressure from Cardiff, they are top of the league for a reason and I thought they played particularly well.
"Even then we still stuck at it and I thought their opening goal was a foul on our goalkeeper.
"The second half we had more of a go than what we did in the first, and with a couple of minutes to go we are still in it but the second goal was a sucker punch.
"To be fair the preparations took a little bit of a hit with a few of them being ill, but hopefully we can get over them in the next couple of days and be ready for Sheffield Wednesday."