Costa was involved in a number of heated exchanges with Stoke players and was shown a yellow card in the 17th minute when he reacted angrily after going down easily during a duel with Bruno Martins Indi.
The Chelsea man then clashed with Ryan Shawcross and Phil Bardsley as the game continued and Hughes was not impressed with the prolific attacker's behaviour.
"Diego Costa is adept at the dark arts and everyone in football recognises that," Hughes told reporters.
"He draws fouls and tries to make the most of contact when they are not fouls.
"We did not target Costa, he targeted our players if anything. I played in that position for many years and you have to react better than that.
"He is an outstanding striker, you can still have that edge, you can still look after yourself but that kind of behaviour, going over too easily and staying down when he was not hurt, does not help."