The Catalan giants bounced back from La Liga disappointment in 2012 by clinching the 2013 title, but the Supercopa de Espana was the only other trophy they could add.
They were embarrassed in this year's UEFA Champions League semi-final – eventual winners Bayern Munich beat them 7-0 on aggregate – and winning Europe's premier club competition is high on the club's agenda again in the new year.
"2014, we ask you to be a year full of tiles," former Arsenal captain Fabregas told Mundo Deportivo.
That is a sentiment echoed by Pique and Alba, with the former adding: "What is certain is that we will give everything."
Left-back Alba acknowledged that winning the Champions League will not be easy, and that they must take it one match at a time.
"(Winning the Champions League)…that is the wish, but to reach Lisbon is simply to go game by game. And the first thing we have to do is remove Manchester City (in the round of 16)," Alba said.
Fabregas also weighed in to the FIFA Ballon d'Or debate, tipping team-mate Lionel Messi, who is one of three finalists alongside Franck Ribery and Cristiano Ronaldo, to claim the prestigious prize in Zurich on January 13.
"If the criterion is to give the trophy to the best in the world, the prize should be for Leo Messi," Fabregas added.
