The Albion forward appeared to make contact with referee Nigel Miller off the ball, causing the official to immediately show him a red card.
Poyet revealed that he had not spoken to his player over the incident, preferring to let him calm down before asking what had happened.
"I'm desperate to jump on the bus to see the DVD and to talk to Ashley Barnes," he said.
"My way of managing this is I prefer the player to calm down because if you go to the dressing room and you ask them straight away then they will put their excuse in there and blame somebody else.
"I'm going to say I suppose it was for talking (dissent). I don't know, I cannot confirm because I did not talk to him yet. I saw nothing, I was looking at the ball."
The result saw Brighton drop out of the playoff places, while Bolton moved to within three points of the top six in the Championship.