The former Motherwell striker, one of the nominees for the Royal Mail PFA Scotland Player of the Year award, apologised for his behaviour and stressed that he has no hard feelings towards his manager.
"It was nothing to do with the team or the gaffer, it was just my passion for playing for the club," said McDonald. "I wanted to stay out and try and turn the game around for the team and myself.
"No player is happy coming off when the game is in the balance but in saying that, my reaction was totally incorrect. I apologised to my team-mates and manager straight after the incident and then again when we went in to the changing room.
"No player should do that and I'm fully aware of that. I'm 150% behind my manager and everyone at the club. The gaffer signed me and has a lot of faith in me and believes in my ability.
"So to clarify, I put my hand up and apologised for what some people would call my petulance."
McDonald added: "Credit to the gaffer and the way he dealt with it. We continue to work together and we go forward from there. It's not the first time you've seen this from a player and I'm sure it won't be the last."