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 ($110 million) 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.