The Macedonian's actions were seen by referee Mark Clattenburg, who immediately sent off the full-back.
Having had time to reflect on the incident, the 28-year-old has felt it necessary to say sorry to everybody connected with the club.
"I want to say a big sorry to all the fans because it was a full stadium of 25,000," he said in a statement on the club's official website. "I've had a couple of good games, was man of the match and Player of the Month in December.
"But I'm not happy with what I did on Sunday. When the referee sent me off it totally changed the game.
"The players were angry after the game, and some of them – the ones who have been a long time at this club - said to me they are disappointed in me. I want to say sorry to all my friends, teammates, to all the physical staff and the coaching staff."
Popov joined West Brom last summer on a season-long loan basis from Dynamo Kiev.