Barcelona under 'brutal' pressure after their golden era with Xavi
The Catalan giants won four editions of the competition between 2006 and 2015, and have endured some humiliating eliminations since.
Barcelona let leads slip against Roma and Liverpool and were thrashed by Bayern Munich in recent years, while they have failed to make it out of the group stage in the past two seasons.
"There is huge demand on us, the bar is so high - this is Barça," Xavi told a news conference.
"This is a consequence of the Barça of the past few years, of our era, as a player. In 10 years, from 2006 to 2015, four Champions Leagues were won."
The coach said the club's objective was to make it through the group phase, ahead of their opener in the competition against Belgian champions Royal Antwerp on Tuesday.
"We like challenges, but the level of demand is so high, it's brutal," he continued.
"It's a consequence of inheriting a brilliant era, the best in the history of this club."
However, Xavi said his players were coping well and excited to start their new European campaign.
"Looking in the faces of the players, the joy, I see hope," added Xavi. "A lot of hope and desire."
Barcelona spent little in the summer as they continue to endure financial difficulties, but were able to sign Joao Felix and Joao Cancelo on loan.
They also replaced Sergio Busquets with former Barça youth team product Oriol Romeu, signed from Girona.
The midfielder, 31, said he did not imagine he would be back at this level after leaving Barcelona in 2011 for Chelsea, later joining Southampton in 2015.
"I'd be lying to you if I said that when you go to Southampton you think you'll be playing a key role at Barcelona (one day), it's hard to imagine," said Romeu.
"Football has many twists and turns. I'm happy, and hopeful of doing a good job."