Suarez joined the Catalan club in a five-year-deal from Liverpool last week despite having received a nine-match international ban and a four-month suspension from all football related activities for biting Giorgio Chiellini in Uruguay's group stage match with Italy.
"We accept that we are all humans and that we have our imperfections; we try to learn from when we make mistakes," said Zubizarreta. "Our history is full of bad days as well as good days. Luis Suarez will be a star at Barcelona although Barcelona is more important than one player."
Suarez, who cost €81m according to the Spanish media, is yet to be presented at Camp Nou because of the ban, which Barca are appealing against. "Luis Suarez is a Barcelona player but, aside from that, we have been told by our lawyers to be discreet," said Zubizarreta.
He added that signing a defender before the end of the transfer window remained a priority for the club. They have brought in the goalkeepers Marc-Andre ter Stegen and Claudio Bravo but have yet to sign a defender. Last season Barcelona struggled at the back and failed to win any major trophies. "This is a necessity for us. Last year we had a good nucleus of centre-halves but Puyol [the retired Carles Puyol] is no longer with us and we will try to cover his loss. Hopefully we will have good news soon," said Zubizarreta, referring to an anticipated deal, at around £16m, for Valencia defender Jeremy Mathieu.