Barton lashed out at Rovers star Pedersen with a blow to his stomach that caused the Norway international to fall to the ground.
Referee Michael Jones did not punish Barton after the incident, which could leave the player open to retrospective action from the FA.
Blackburn boss Sam Allardyce opted not to give his thoughts on the matter after the game, instead leaving the FA to deal with it.
"I'm not really going to talk about that because I don't want to detract from our victory," he said.
"Whoever will see it will see it and do whatever needs to be done."
Pedersen offered a similar view, adding: "You saw the pictures. I don't want to speak much about it now."