The 21-year-old, who was standing in as captain for the absent Scott Dann, was dismissed after Blackburn had taken the lead in the first half for clashing with Nick Powell.
Bowyer said on Sunday that he would review the incident and now he has confirmed that no appeal will be made by the Lancashire club.
"I got to see the sending-off myself and we're not appealing it, that's for sure," Bowyer told BBC Radio Lancashire.
"I don't think he's actually meant to do what he's done. He just try to shrug him off - he said that himself - but he's accepted that you can't raise your hands.
"He was gutted because he now misses three games and he might not get back into the team with Matt Kilgallon and Scott Dann forming a partnership."
Blackburn lost the game in the dying seconds when Emmerson Boyce headed home to make it 2-1 to the Latics.