"It was one of those games that could have gone either way. It went to the TMO and sometimes you get them and sometimes you don't," said Cullen.
"We got it there today and that was the difference between the two teams.
"That was right up there with any European game I've played. It was pretty intense out there.
"Clermont are a great team and it's a big win for us, coming over here to beat them."
While Cullen and co were clearly delighted to have reached a third final in four years, the former Leicester Tigers lock insists the mood in the dressing room wasn't one of pure delight.
Cullen praised his team's character in coming back from a half-time deficit and in seeing out a barrage of attacks in the final stages but the 34-year-old suggested luck was on Leinster's side.
"There was more of a sense of relief in the dressing room afterwards," added Cullen, who lifted the Heineken Cup in 2009 and 2011 having tasted defeat in the 2007 final.
"There's a feeling that we got out of jail a little bit. There were times when we were a little bit inaccurate.
"Our discipline in the first half cost us a bit. We looked okay when we were defending, although they did breach us a couple of times.
"Everyone dug in pretty well and showed good character, though, especially going in six points down at half time. There's quite a bit of belief in the team and there wasn't really much panic at that stage.
"Both teams made quite a few mistakes considering the quality of the players out there but I think that had a lot to do with the pressure."