Marcos Alonso fired the game's only goal, a superb long-range strike, to take Wanderers within three points of the play-off places that they tipped the Seagulls out of.
In the final seconds of injury-time, Barnes appeared to make contact with referee Nigel Miller off the ball and was immediately shown a red card.
As with many in the stadium, Poyet's eyes were up with play and he explained Barnes was being allowed a cooling-off period after the match but would be asked to provide an explanation on the long trip back to the south coast.
"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."
- Sports & Recreation
- Ashley Barnes