And while the nature of their finishing and the expansive style favoured by arguably the continent's greatest-ever team may have hogged the highlights throughout a sublime European campaign, Cullen believes the basics played a huge part on the biggest of days.
"It was an area we targeted. In the semi-final, the lineout was the area that probably could have lost us the game, and the scrum as well at times," said Cullen.
"In these big games you can't afford not to have a good platform. Our platform was good in the final.
"We scored off a turnover from a scrum and we got a penalty try off a lineout maul from 20 yards out. They're two massive parts of the game. That goes a hell of a long way to trying to win the match."
As well as dominating the tight exchanges at Twickenham, Leinster were also far more clinical than the 1999 champions.
Whereas Ulster failed to take their chances in the opening half hour, Cullen and co made the most of almost every opportunity that came their way.
Ulster skipper Rory Best admitted his side "were given a lesson in how to create five or six chances and take every single one", and that's pretty much how Cullen saw it too.
"We knew it was going to be pretty tough out there. I thought they really put it to us in the first 30 minutes. They created a couple of chances that they just didn't nail," added Cullen.
"We went up the other end and got our two tries and that was the difference in the first half.
"In finals sometimes it's just about getting a lead. If we learnt anything from last year (Leinster were 22-6 down at half-time against Northampton), we knew we just had to keep playing, no matter what the situation. We're just delighted to win the game."
Excelling on the greatest club stage of all appears to have become second nature for Leinster these days, with three titles in four years and a semi-final appearance in 2010.
But it wasn't always that way.
For so long Leinster were known as underachievers, as the nearly men of European rugby.
Yes, there were plenty of quarter-finals and semi-finals prior to their first title-winning campaign of 2009, but they always ended in disappointment.
It was a trend that Cullen couldn't see changing and it prompted him to move to England to join up with heavyweights Leicester in 2005. The switch across the Irish Sea not only broadened his horizons, it also taught him a lot about the nature of winning big games - something that he and his team-mates began to take to a whole new level after he returned to Dublin in 2007.
"We had crashed out of Europe pretty embarrassingly on occasions and I didn't see how the side would ever be successful.
"I had a hunger to be with a successful team. Leicester are a fantastic club with a winning mentality. I can't say enough about what happened there.
"There's something special about playing for the team you grew up supporting, but when I was at Leicester I learnt a huge amount about what is required at this level.
"Even in 2007 I couldn't really see how the team was going to be successful. But Michael Cheika then came in as coach and changed the mentality. He brought in some quality players and some good young players came through as well.
"It wasn't pretty when we won the Heineken Cup in 2009, we sort of fell over the line in the final against Leicester at Murrayfield, but the belief was there and we knew we had to kick on after that.
"(Current head coach) Joe Schmidt brings a relentless pursuit of excellence. He demands high standards, and it's great for the players. All the coaching staff work so hard with this squad.
"There's a really good mix in this team. Everyone gets on well and it's a really tight group. Everyone's happy to work for each other and everyone works hard. It's an enjoyable place to be."