Brendan Rodgers threw the armband to a key figure in his side on occasion when regular skipper Steven Gerrard was unavailable.
Suarez appeared to be a wise choice for the role, as a talismanic presence and a man famed for his whole-hearted approach to every fixture he takes in.
The 30-year-old has, however, claimed that he is “quite shy” and not a born leader.
He considers himself to be more of a team player, with the focus locked on the likes of Lionel Messi and Neymar at Camp Nou helping him to shine away from the limelight.
“I like the low profile, to be a player among the others,” Suarez told France Football.
"I am there to give a helping hand to the team but taking decisions, that is not really my thing. At Liverpool, I had the chance to be captain and it was not easy for me.
"Even if people find it hard to believe, I am quite a shy person. I am not used to pushing myself forward."
Suarez did take in a 5-0 victory over Tottenham at White Hart Lane while skippering Liverpool, but also suffered a 3-1 defeat to Cardiff at Anfield.
He may have experienced mixed fortunes while leading the Reds, but a distinguished career has delivered plenty of success and Suarez is happy with what he has achieved and his standing in the global game.
“There are players who are more marketable than me, more gifted with the media, but that does not bother me,” Suarez added.
“The individual titles that I have been able to win, I got them on the pitch thanks to my performances and the help of my team-mates.
"In England, I had the luck to be recognised at the same time by the players and the press (PFA and FWA Player of the Year in 2014). At the international level, I know there are players who are above me. But that is not something that bothers me.”