The Premier League side - who have been in fine home form this season under Manuel Pellegrini - host the Catalans on Tuesday in the first leg before a return clash at Camp Nou in March.
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"These knockout games are complicated because after a while you have to get into competition and start worrying about the opponent," he is quoted by Marca as saying. "We'll have to work hard.
"We've learned from last year but it's worth bearing in mind that Paris Saint-Germain and AC Milan were no walkovers. We know that Manchester City are going to require a lot of effort to beat."
Zubizarreta also condemned the mecherazo incident in which Real Madrid forward Cristiano Ronaldo was hit on the head with a lighter in the Atletico Madrid Copa del Rey clash, suggesting fans need to put football into perspective.
"We all have to remove the tension in the stadium, where it seems like every game is the end of the world," the Barca transfer chief added.