While the Liga champions were able to bring in Neymar from Santos, they failed to sign a centre-back, leaving head coach Gerardo Martino with just Carles Puyol and Gerard Pique available.
Gerardo Martino's men were linked with a move for Paris Saint-Germain's Thiago Silva but failed to agree a transfer, although Zubizaretta is content with the club's transfer activity.
"In the history of Barcelona, the signing of a centre-back has always been complicated," he explained.
"We have the squad we wanted and one that will be able to compete extraordinarily well."
Barcelona conceded their first goals of the league campaign on Sunday in a 3-2 win over Valencia.
Captain Puyol is nearing a return from knee injury while Zubizaretta confirmed talks are ongoing with youngster Marc Barta in relation to a new deal.
"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," Zubizaretta added.
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