Tempers flared at full-time after the Bluebirds secured a valuable 1-0 win at Oakwell on Wednesday, which condemned Barnsley to their fifth consecutive Championship defeat.
Reds assistant coach Joseph Laumann was first shown a yellow card for trying to confront Morison in the dugout area before he followed him to the tunnel and appeared to shove the former Wales international, triggering a brawl involving players and staff.
Morison told The Star Laumann ‘picked the wrong person’ - but insisted it was just ‘handbags’.
"The security got involved and it all just boils over,” he said.
"It’s handbags really, at the end of the day, but play fair and things like that don’t happen.”
Cardiff had accused Barnsley of ‘cheating’ after ex-Rotherham midfielder Will Vaulks got into an altercation with a ball boy during the second half when the youngster hid a towel under his jacket which was being used to dry the match ball before the Cardiff man’s trademark long-throws.
Another towel was hid behind a partition wall separating the pitch from the stand in the first half.
“It is cheating but karma comes back and bites you in the ar*e,” added Morison.
For their part, Barnsley accused Cardiff of lacking ‘sportsmanship.
Boss Poya Asbaghi said: "It was ridiculous, the way they behaved.
“I have never complained about a coach that is standing on the side and just screaming all game.
"It’s part of the game, I know, but after the game show a little bit of sportsmanship.”