Sarries will begin the defence of their domestic title against Worcester in the London Double Header at Twickenham on Saturday, 3 September.
Barritt told BBC Radio London: "Last year was probably the most successful season in the club's history.
"But we now have a fresh page to write a new chapter in the Saracens story."
England centre Barritt, 29, played a key role in Saracens' momentous campaign, which culminated in their 28-20 victory over Exeter Chiefs in the Premiership final at Twickenham on 28 May.
Two weeks earlier, they were crowned European champions after beating Racing 92 in Lyon, becoming the first team in the competition's history to win all nine games in the tournament on their way to picking up the trophy.
However, Barritt believes they could face an even tougher challenge next time around.
"This Premiership shows you that anyone can beat anyone on their day. You can't be fooled into any false sense of safety that it's just going to happen," he said.
"The Premiership is the most competitive domestic league in the world. There's quality throughout and every team brings equal and different challenges."
Barritt also said the "continuity of the squad" - of which eight were part of England's Six Nations-winning squad earlier this year - has been "a huge key" in their success.
"We've been a very settled squad who understand each other, who've played together for a certain amount of time, and that's allowed those bonds to grow," Barritt added.
"You can see by the intensity of training and the focus in the players' minds that the guys are very eager to make it another successful year."
Meanwhile, Saracens are learning from the success of Australian Football League club Hawthorn Hawks as they seek to deliver another trophy-laden season.
Hawthorn have won the last three AFL Championships and sit top of the table as they bid for an historic fourth in a row.
"We've looked specifically at the Hawthorn Hawks in the AFL, who are [aiming for] a fourth championship in a row," Barritt told BBC Radio 5 live.
"It's about the relentlessness of the organisation. It's about an organisation being hungry and being as driven as they have ever been, as if it's their first championship.
"We are back-to-back Premiership champions and (now) European champions. We know those things don't come easily, and we know the next season is going to be that much harder because you are going to have a target on your back."

She replaces Jo Stevens, who resigned last month in protest at an instruction that Labour MPs should back the bill to trigger Brexit.
Ms Rees is the fifth appointment to the role since the 2015 general election.
Mr Corbyn said his team's strength would "develop Labour's alternative plan to rebuild and transform Britain".
In other appointments, Rebecca Long-Bailey becomes shadow business secretary, Sue Hayman takes the environment, food and rural affairs brief, and the new shadow chief secretary to the Treasury is Peter Dowd.
Ms Rees was a shadow justice minister in January 2016 but resigned after the EU referendum, only to return to the job in October 2016.
She backed Andy Burnham for the Labour leadership in 2015 and Owen Smith in 2016.
A former Welsh squash international who won more than 100 caps, the new shadow Welsh secretary was preceded by Ms Stevens, Paul Flynn, Nia Griffith and Mr Smith.
Ms Rees was previously married to former Labour Welsh Secretary Ron Davies.
Christina Rees is the fourth MP to hold the shadow Welsh secretary's job under Jeremy Corbyn - and the fifth since the general election less than two years ago when she entered parliament.
She supported Owen Smith's challenge to Mr Corbyn's leadership last year but voted with the Labour leader to trigger Brexit this week.
Eight Welsh Labour MPs rebelled in that vote, including Shadow Arts Minister Kevin Brennan.
Unusually, the Cardiff West MP and other frontbench rebels are likely to keep their jobs, a sign of Mr Corbyn's limited authority as leader.
Premiership and European Champions Cup winners Saracens are determined to be even stronger next season, says skipper Brad Barritt.
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Labour leader Jeremy Corbyn has named Neath MP Christina Rees as the new shadow Welsh secretary.