Tykes, who have won just once in their last 26 league games, created the better chances but were made to pay for their failure in front of goal.
However, tempers frayed after the final whistle when there was an altercation between Morison and a member of the Barnsley coaching staff as they headed towards the tunnel.
Swedish coach Asbaghi - who is still awaiting his first league win since taking over in November - said: “To be totally honest, I knew when I came to England I’ve heard that I have to be ready for the verbal communication from opponents.
“It is going to be different to what I'm used to.
“We don’t argue as much and complain or scream at each other.
“But for me, I like that. It's a charming thing with England. It’s a fun thing.
“But it has to stop after the final whistle. They can scream and have intensity during the game and I don’t complain.
“But if you are a coach of Cardiff, and given the way you have just won the game one zero, then at least come and say ‘thank you’.
“We went to him and said ‘thank you, congratulations for the victory’.
“I’m not going to say what he said but it was some really bad things without any of us saying anything.
“And then my assistant coach reacts to what he says. Of course. That's normal.”
The pair had to be seperated by stewards.
Asbaghi added: “After the game it’s over.
“If you win, win with style. Congratulations to Cardiff.
“But they didn’t win with style today. After the game, show some sportsmanship please. It was ridiculous.”
Asked for his view on the events, Morison said: “They didn’t like it - we beat them.
“I don’t think they covered themselves in glory with the way they physically hid the towels on the edge of the pitch and put them up their ball boy’s tops.
“It is cheating but karma comes back and bites you in the ar*e
“I made my thoughts clear at the end and they didn’t like it.
“He followed me down the tunnel and wanted to have a pop at me.
“But he picked the wrong person.”