Exeter boss Rob Baxter highlighted the two yellow cards sustained by his side as the reason for their collapse against Cardiff Blues.
The Chiefs lost two backs in a matter of minutes as Ian Whitten and Sireli Naqelevuki were sent to the bin, reducing them to 13 and giving the Blues the extra space needed to accumulate enough tries for a bonus point.
Exeter had been utterly rampant for the opening 50 minutes, racing into a 41-3 lead thanks to six tries including by six different scorers, started by England international Tom Johnson.
The win meant that Exeter kept pace with champions Toulon at the top of Pool 2, as they look to make the knockout stages of the tournament for the first time in only their second season.
"I think it doesn't matter who you play, when you go down to 13 men you put yourself under a bit of pressure and we got ourselves down to 13 men pretty unnecessarily," said Baxter.
"That flipped the whole game. Going down to 13 men, you are going to struggle a little.
"In the first half we played with real intent and the attitude that we took on to the pitch following last week was absolutely fantastic - not just a good attitude to attack the game but also the physicality and strength of the carries.
"Obviously the battle for us is to keep the quality for longer periods and when you end up on the defensive side, you don't end up conceding a couple of relatively soft penalties for a knock-on and an across-the-chest tackle.
"To give up a couple of those when you don't need to is a bit frustrating."