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."
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.
