Dickov was shocked Dons defender Antony Kay got sent off for lashing out at Robbie Simpson because the pair are apparently "good mates".
Goals from Darren Potter and Daniel Powell handed the Dons a routine 2-0 opening-day victory at stadium:mk before the pair squared up at the final whistle.
Dickov admitted the brawl took him by surprise as Simpson and Kay - making his home debut - were the best of friends before the match.
He said: "There was an elbow on James Tarkowski about two seconds before it and tempers were flying a little bit high. It's a sad one because Robbie and Antony Kay are good mates.
"I didn't see it, but the referee has sent one off and not the other on the view of the linesman, when really I think the referee is closer.
"It was a bit surprising, but I've played against mates before as well and when you're out there it doesn't matter. One thing I will say is that Robbie and Antony Kay aren't malicious or nasty people, they're good kids who want to win football matches."