Suarez joined the Catalan club in a five-year-deal last week from Liverpool despite receiving a nine-match international ban and a four-month suspension from all football related activities for biting Giorgio Chiellini in Uruguay’s group stage clash 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 81 million euros (64.22 million pounds) according to Spanish media, has yet to be presented at the Nou Camp due to 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.
Zubizarreta added that signing a defender before the end of the transfer window remained a priority for the club. They have brought in keepers 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 trophy.
“This is a necessity for us. Last year we had a good nucleus of centre-halves but (the now 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.
Barca are believed to be close to agreeing a deal with Valencia for Jeremy Mathieu.
"Valencia received our proposal and now they have to make a decision,” said Zubizarreta.
“It is a problem for 80 or 90 percent of the big clubs who are looking for players in this position. On certain occasions we have not been able to arrive at agreements that we wanted."
(Reporting by Tim Hanlon, editing by Pritha Sarkar)
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