Leinster were crowned champions for a third time in four years at Twickenham, a level of sustained success that is unmatched in European history, even by four-time winners Toulouse.
"It will take a couple of days for it to properly to settle in but after we won one we talked about not being content with that and trying to create some sort of dynasty and something to be remembered by," O'Driscoll told Sky Sports 3. "We're going in the right direction towards doing that but I know this team will be hungry for more."
Leicester are the only other team have successfully defended their Heineken Cup title and Leinster did it by breaking three records. Not only did they crush Ulster with the biggest winning margin in Heineken Cup final history, but Leinster set a new record for points scored (42) and tries scores (five).
Sean O'Brien and Cian Healy scored first-half tries to put Leinster in charge and they sealed the victory with a penalty try plus late touchdowns from Heinke Van Der Merwe and Sean Cronin.
Fly-half Jonathan Sexton converted all three tries and kicked three penalties for a personal haul of 15 points as Leinster added the 2012 title to those they won in 2009 and 2011.
O'Driscoll added: "That's why it's enjoyable, You're going in day-in and day-out because you know you're going to be pushed by the guy next to you. We played for one another out there and that really showed today.
"The energy from all 23 was phenomenal, it shows where we are as a squad. I only came in for the knockout stages. For the important part, but the hard graft was put in during the group stages."
Leinster captain Leo Cullen lifted the trophy for a second time and compared his emotions to those of Masters champion Bubba Watson.
"To quote Bubba Watson, I haven't got that far in my dreams," Cullen said. "There is something special about playing for the team you grew up supporting. That is the team you want to represent more than anything. Success with this team means the world to me."