The Spanish champions were chasing Thiago Silva but the Brazil captain opted to stay with Paris St Germain in France's Ligue 1 and Barca's only major signing was Silva's international team mate and forward Neymar from Santos.
Defensive weakness was cited as one reason for last year's failure in the Champions League and the back four looked far from assured in Sunday's 3-2 La Liga win at Valencia.
Zubizarreta told a news conference on Tuesday the club was closely observing the market, raising the prospect they could move for another centre back in the January transfer window.
The former Spain and Barca goalkeeper said the imminent return of captain Carles Puyol from injury was as good as a new signing and added the club was in talks with Marc Bartra on extending his contract beyond the end of the current season.
"We have the squad we wanted and one that will be able to compete extraordinarily well," Zubizarreta said.
"In the history of Barcelona, the signing of a centre back has always been complicated.
"We are always focused on making the squad the best it can be and I am delighted to have the chance to do my job."
Barca, who are bidding for a fifth title in six years, top the La Liga standings on nine points after winning their opening three La Liga matches and claimed the Spanish Super Cup against Atletico Madrid last week.
They have been drawn in Champions League Group H with fellow former winners AC Milan, Ajax Amsterdam and Celtic.
- Sports & Recreation
- Thiago Silva
- La Liga