"We were going for a treble at Twickenham against Wasps and we were beaten. I don't want history to repeat itself and leave me with a similar empty feeling," said Cullen, who is bidding to become the first captain to lift the Heikeken Cup three times.
"We are looking for a third Heineken Cup win in four years on Saturday. I remember the feeling of relief when we won the first time in 2009 and then the sheer euphoria after our second half comeback last year.
"When you experience success it makes you greedy for more and we want to experience that same feeling of 2011 again this weekend."
But Cullen knows that Ulster will be every bit as tough as Northampton Saints were in Cardiff last year and Leicester Tigers proved when he first led Leinster to victory at Murrayfield in 2009.
"They have a very strong pack, pace outside and a strong kicking game. And in Ruan Pienaar they have one of the stand-out players of the tournament," added Cullen.
"We have plenty of experienced players and we just need to concentrate on ourselves. We know that if we get things right we are going to be a hard team to beat.
"The start of the game is crucial. Ulster were 19 points up in no time against Munster and we can't afford that to happen to us."