They now play the Ospreys in the RaboDirect PRO12 final at the RDS in eight days time with coach John Schmidt declaring: "We have got a bit left on our plate and we will now focus on that final give that our best shot.
"I would like to think we can select from a full squad, no-one pulled up to badly, and we know that anyone who can beat Munster 45-10, as the Ospreys did, have to be a very good side."
No-one has done the domestic and European double since London Wasps in 2004 and full back Rob Kearney added: "We have a good opportunity ahead of us to do something really special and if we can win on Sunday that will be special."
But even with the margin and manner of their Heineken Cup treble Schmidt was adamant that Ulster had given them a real run for their money.
"It was tough going for the first 60 minutes when we could not get the ball back from them for long periods," he said.
"It was pivotal that we scored immediately after their try but we still let things slips a bit in making some small errors that made it a little tougher for ourselves.
"When we went to Montpellier six months ago we were just one of 24 challengers, we were not thinking about defending the title, and that is how it will be again come next season."
Leo Cullen - the first player to captain a team to three final triumphs - put that down to "a real good mix in the team, it is an enjoyable place to be and I am just delighted with the win.
"In the first 30 minutes they really came at us and the difference was that we took our two chances we had before half-time."
Ulster, appearing in only their second final after being crowned European champions in 1999, rued the chances they let slip when they were taking the game to the champions.
"We started exceptionally well but you have to take your chances," said coachBrian McLaughlin. "Leinster's defence was rock solid and they did a fantastic job and the two scrums we lost came back to haunt us.
"The scoreline may have flattered them a bit but give Leinster and inch and they will take a mile and we have to learn from this.
"We have worked very hard over the last three years to make ourselves a quality rugby-playing side and we tried to play a bit of football."
Hooker Rory Best added: "We came full of confidence and belief but we have had a bit of a lesson in taking your chances. They make you do things you would not normally do in a tight game and then you find you are chasing them.
"There is no point in looking for excuses - they are a very good rugby team. It was heart-breaking to see Leinster lift the trophy and we have to use that to drive us one."