The London side were crowned champions of Europe for a third time in four seasons after coming from behind to beat holders Leinster 20-10 at St James’ Park.
A brutal contest in front of a 52,000 crowd ended with Saracens becoming the most successful English club in European Cup history.
O'Driscoll, himself a three-time winner of the competition, paid tribute to Mark McCall's side, who are now a step closer to a second league and European Cup double in three years.
The English champions made an eye-watering 224 tackles in the game, with captain Brad Barritt leading by example with a game-high tally of 28.
"It was a lot about brutal defence but it was more than that," said O'Driscoll.
"The intensity of their performance was unbelievable. That second half, they came out and just blew Leinster away and Leinster couldn’t live with any aspect of their game.
"Brad Barritt and Alex Lozowski were outstanding in the centres.
"They pride themselves on their defence and their togetherness and it really showed today.
"They should be incredibly proud of what has been an outstanding campaign, not just today, but their season in general."
Barritt was named man of the match for his colossal stand in defence, but O'Driscoll was also keen to single out Billy Vunipola's contribution.
Vunipola was booed most times he touched the ball during his team’s semi-final victory over Munster and the England international again received jeers.
He was handed formal warnings from his club and the Rugby Football Union for a controversial social media post but the 26-year-old let his rugby do the talking on Saturday afternoon, scoring one of his side's two tries in the 20-10 victory.
"Billy Vunipola had another monster performance," said O'Driscoll.
"His stats were incredible: 20 carries and nearly the same in tackles. There’s no doubt he’s a big-game player.
"He gave them the momentum and go-forward, even on static ball, which any team would cry out for."
Leinster, at one stage 10 points to the good in the first half, enjoyed the majority of possession but struggled to break down the red wall of Saracens defenders.
Despite losing Maro Itoje to a first-half yellow card and Titi Lamositele through injury, the Gallagher Premiership outfit had enough strike power across the pitch to bludgeon Leinster into submission.
"Look at the power and the size of their pack… I know Mako Vunipola went off early but there was still George Kruis, Maro Itoje, Will Skelton, Jamie George. That pack is brutal, it’s an international-style pack.
"Leinster just couldn’t deal with Saracens’ power game. The power game won out.
"It’s one thing knowing what to expect but it’s another thing stopping it."
The 2019 Champions Cup final had been billed as the battle of the fly-halves as Lions team-mates Jonathan Sexton and Owen Farrell renewed their individual rivarly.
But it was the England man who emerged victorious from the duel, as Sarries avenged their defeat to the in Irish side last year's quarter-final.
"Sexton was snuffed out every time he got the ball," said O'Driscoll, who won three European Cups alongside the Leinster captain.
"Some of those read-throughs in defence from the likes of Kruis were just phenomenal.
"He got hit back on his heels a number of times and never really got into a groove. But also, he didn’t really have a platform to play because of the intensity of those collisions.
"Sarries were dominating the collision zone. It was very hard for him to play on the front foot and rugby’s a hell of a lot easier on the front foot."
The result means heartbreak for Leinster, who were bidding to become the first team in European history to win five Champions Cups.
According to O'Driscoll, his old side can have few regrets after being out-fought and out-played by the better team on the day.
"It’s almost easier for Leinster to take because they can’t say ‘we were robbed’ or ‘we really should’ve found a way to get it done’ they were just out-played.
"Leinster weren’t at their best but they weren’t allowed to be at their best at the same time."
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