He was particularly irked by Zack Fitzgerald, who was ejected from Sunday's game for his behaviour as he served time in the penalty box.
In all, the American received 38 penalty minutes, for offences including unsportsmanlike conduct and abuse of officials.
"I thought we took some stupid unnecessary penalties, especially in the third period" said Thompson.
"Zack took a couple of bad ones...he's been doing a great job for us but I am not going to put up with that."
Asked what he meant by that, the coach replied: "I am not going to put up with it, guys won't play. Simple as that.
He said the team had to "dig him out" by playing short-handed and earning the 5-2 win.
"We have got to be cool because that power play (Cardiff's) has destroyed us all year.
"And we handed it on the plate to them to get back into the game. But we did enough to get through."
Thompson accepted Fitzgerald had been frustrated in the box because officials did not act an infraction on Jonas Westerling as he skated through the middle.
"It was a cheap call from the referee - but we have got to be smarter because we know against Cardiff Devils we are not going to get that advantage."
Overall, though, the team boss said he had been pleased with the battle-level in both weekend wins.