He, however, said that fellow teammate, Lionel Messi ‘deserves many more Champions League titles than he has’.
Messi has four winner’s medals to his name since 2005, the most recent of which came in 2015 when he helped the Catalan club to a 3-1 win over Juventus in Berlin.
“The Champions League is the competition which defines you, as the best players and teams of Europe are in it,” Suarez told RAC1.
“There’s an extra motivation to never relax. Our desire, motivation and expectations are for this to be a great year.
“It’s obviously an irritation when your rival [Real Madrid] has won the past three Champions Leagues, as it’s historic.
“It gives you even more desire to turn the situation around.
“[Messi], as a player, deserves many more Champions League titles than he has. He is full of desire after the World Cup and after what happened to us in the Champions League last year. He has always taken on a leadership role and is keen to lift some trophies.”
Barca have been drawn in a group with Tottenham Hotspur, Inter Milan and PSV Eindhoven for the 2018-19 edition of the competition.