"It's obviously a great occasion and it's great to be a part of these days," said Cullen, who was a Heineken Cup runner up with this weekend's opponents in 2007.
"There's a big pressure but it's more excitement about looking forward to the game and looking forward to the challenge.
"It's very easy to be caught up in the occasion but it's important that we concentrate on our performance. We've done our work on Leicester and tried to analyse where we perceive their strength and weaknesses to be but it's just about implementing our game plan and taking the opportunities that, hopefully, we'll create."
Leinster made a mockery of their underdog tags to crush tournament favourites Munster 25-6 at the semi-final stages of the continent's premier club competition earlier this month - a feat Cullen feels his team will have to repeat if they are to overcome the newly-crowned English Champions.
Cullen believes Leicester will start as favourites in Edinburgh but the 31-year-old second row has more than enough faith in a side that he says have already proved their doubters wrong.
"In many ways, the pressure will probably be on Leicester as the favourites because they've been in this position before whereas we're the novices, as such," added Cullen.
"A lot of people are surprised that we're in this position, but when we set out or goals at the start of the season, we wanted to be a part of these big days. We'll be very disappointed if we don't win the game so I think we do have a lot to lose.
"I've always had belief in the squad of players we have. It was just about pulling performances together and bringing a bit more consistency to our game.
"It hasn't always been the prettiest at times during the tournament but we're still hanging in there and I think there will be times in the game where we'll have to hang in their too."