A number of Stoke's defenders - most notably Ryan Shawcross and Bruno Martins Indi - had run-ins with the Spain international, whose temperament has been called into question during his Chelsea career.
Costa picked up an early yellow card for dissent but was otherwise able to keep a lid on his emotions, although Hughes argued that it was the striker who targeted the defenders rather than the other way around.
"We didn't target him, more likely he targeted our players. I played in that position many years and I look at his qualities as a striker, he's an outstanding striker, but on occasions he's got elements of his play that he doesn't really need to have," he told reporters.
"You can still have an edge, an element where you can look after yourself, but you don't have to have the rest.
"I think it takes away from his performance and his image as a player, it's not necessary. Maybe that's how he generates his feeling in the game and when he's able to produce his best work. I think it detracts from what a good player he is."
Stoke's defeat leaves them still ninth in the Premier League table, but now seven points adrift of the top eight.