The former Spain international freely admitted that while the Blaugrana defended well against the Rojiblancos, they did not create enough opportunities to earn a victory.
The top-of-the-table clash failed to live it to the pre-match hype, with chances few and far between during the course of an underwhelming 90 minutes at the Vicente Calderon.
Zubizarreta commended Gerardo Martino's men for their defensive solidity but admitted that they were rather blunt from an attacking perspective.
"Neither team dominated the match sufficiently to win it," the former Spain international told Canal Plus. "We had the ball but could not find the space to create chances. The work of the back four was very good, as was [midfielder] Sergio Busquets. We were very solid in that regard.
"Sometimes you have games like this where you have to take advantage of the few chances you have to score a goal."
The draw means that Barcelona and Atletico are now just three points clear of Real Madrid, which battled to a 1-0 victory against Espanyol on Sunday.