"I do not have the happiest of memories of Twickenham - I lost a Heineken Cup final there in 2007 with Leicester - and hopefully we can produce the goods this time," said Cullen.
"Losing a Heineken Cup final is not the nicest of feelings.
"Leinster are very hungry to succeed, there are a lot of very ambitious players in the squad and it would be great to achieve those back-to-back Heineken Cup titles but we are just focusing on the process and training hard on a daily basis.
"As long as we can control things that are within our own control we can go a long way to being successful."
Leinster have got to Twickenham the hard way, having to beat ASM Clermont Auvergne in Bordeaux in a semi-final thriller, but indiscipline nearly cost them dear.
"Coach Joe Schmidt drives our discipline pretty hard and it is something he has really pushed - giving away penalties can be hugely detrimental in the big games," added Cullen.
"Against Clermont it was our discipline that nearly killed us in the first half. We gave away four shots at goal and Brock James kicked the lot and we suddenly found ourselves 12-6 down. Our discipline was quite poor and that is something we have to work on and be aware of against Ulster.
"I thought we were pretty fortunate in France, it was all about the small margins in the big game. Because, although I thought we did defend pretty well, Wesley Fofana got across the line and, but for a ball placement, we would have been sitting watching the final and not playing in it.
"We kind of fell over the line - which just goes to show how precise you have to be in these games."
Leinster go into the final unbeaten in this season's tournament with seven wins and a draw - plus the season's Pro12 double over their opponents - but Cullen insists it will be a one-off in the final.
"It's great for the Irish game to have two clubs in the final, the Irish supporters just love the Heineken Cup and every time it comes around you can see interest levels rising.
"Ulster were the first Irish team to taste European success and they reached the knock-out stages last season so we know they have pedigree in Europe.
"When we played Ulster a few weeks ago they were missing a few key players and we scraped a win. It was pretty ugly as the pitch got very heavy up at Ravenhill and it was a bit of a dogfight.
"But Ulster have done amazingly well this season, signed some really quality players in the last few years and under coach Brain McLaughlin they have built up a really good squad.
"I know Brian pretty well and I am happy that he has had a lot of success with this team, he's a really good fellow, so it's going to be a pretty formidable challenge.
"Everyone gets very excited at this time of the year but, as you have put in so much work to get to this stage, it is just about performing on the day. It's an exciting time to be involved in these big games.
"I was involved in some pretty dark days with Leinster, days when we let ourselves down on the big occasions, and those memories are hard to wash away but the young guys coming through have brought such enthusiasm and a competitive edge."