Both managers insisted they did not see Swansea first-team coach Alan Tate grab Birmingham midfielder Jon Toral by the throat during a 0-0 draw at the Liberty Stadium.
Tate grabbed Toral at the end of the first half and both sets of players and coaching staff piled in to the melee which followed.
Former defender Tate escaped a red card from referee Gavin Ward, but the Football Association have the ability to review the incident if they decide it requires further punishment.
"I didn't see anything because I was in the tunnel. The only thing I told the players at half-time was to forget what happened," said Blues boss Aitor Karanka.
"I don't care about what happened – the players showed their spirit on the pitch. If the referee has seen something and not done anything then I don't think he's doing his job."
Swansea head coach Steve Cooper joined Karanka in claiming he didn't see Tate put his hands on Toral despite it causing a mass bust-up.
"It certainly didn't carry on down the tunnel because I went down there. Afterwards it was fine – no dramas. I haven't spoken to Alan," he said.
Both teams struggled to create clear-cut chances, but former Cardiff goalkeeper Neil Etheridge marked his first Blues start with a smart stop to deny Marc Guehi at the death.
"I'm really pleased because this was another really good performance," said Karanka. "I could see a really committed team on the pitch with an amazing attitude.
"It's time to build and the main step in the building process is to have that commitment."
A draw means both Swansea and Birmingham have taken four points from their first two games of the new Championship season.
The Welsh side have kept two clean sheets, but Cooper admitted his team are desperate for a new striker. He added: "We haven't got an out-and-out established number nine in the squad at the moment. It's difficult to get the player we want when we haven't got any money to spend.
"We're frustrated not to win the game and I think we always should be if we don't win home games. I don't think it was from a lack of trying. I think we did have some good moments in the game.
"I know the goalkeeper has made an excellent save from Marc fairly late on and I know we got into good positions where we flashed balls across the box, but our frustration is we didn't do more with the good positions we got in.
"We should be pleased with another clean sheet. They're not the easiest thing to do in this league. I do think there were games like that last season that we lost."