Max Power has apologised after seeing red for the second team this season.
Power said he put his team 'under unnecessary pressure' after kicking out midway through the second half.
The 25-year-old did not make contact but was shown a straight red.
Jon McLaughlin saved the resulting penalty from Jack Payne as the Black Cats held out to win 2-1.
Power, who was wearing the captain's armband for the second game running, will now serve a four-game suspension.
However, with a Checkatrade Trophy game in that spell, he will effectively miss five matches with the first round of the FA Cup scheduled to be played on November 10th.
Power wrote: "Firstly I’d like to say well done to the lads for getting the 3 points today. I put them under unnecessary pressure and could of cost the team a huge 3 points.
"Secondly, sorry to the players, staff and fans who travelled in great numbers for my actions. I was being trodden on and I’ve reacted in the worst possible way which is resulted in a red card. I’m gutted and take full responsibility for my actions.
"I play with my heart on my sleeve and I’m desperate for us as a club to have a successful season. I’ll learn from this and do my best to make sure it never happens again."
Sunderland appealed after Power saw red in the 1-1 draw with Oxford United earlier this season but manager Jack Ross hinted that they are unlikely to do so again.
"I didn't see it at the time. But we understood from the fourth official that it was a kick out. I have watched it and it is a kick out.
"There is no contact and quite a bit of contact between their player. But in fairness to them, they don't react in any way other than to draw the referee's attention to it.
"They don't to pretend to have been caught by it. The ref was looking straight at it too. There was zero contact but it was a kick out.
"When you do that, then you give the referee a decision to make."
It was Sunderland's third red card of the season after Bryan Oviedo kicked out during the 2-2 draw with Peterborough earlier this week.