James Rodriguez made it 2-2 in the 85th minute as 10-man Real Madrid drew level in the La Liga clash, only for Lionel Messi to come up with a 93rd-minute winner for Barcelona to send Luis Enrique's side top of the table.
Zidane has admitted that his team 'needed to use their heads a little bit more' in the latter stages of the contest, with Barcelona's winner coming on the counter-attack after the hosts had pressed forward.
"We can't be happy, we did a lot, all through the game, we had a lot of chances to put the match in our favour. When you don't kill off the game, it can pass you by and that's what happened. We're disappointed with the result," Zidane told reporters.
"When you get to 2-2 with 10 men, you need to use your head a little more and defend closer together. We thought we could score the third goal, but we were out of place from a throw-in and what happened, happened.
"Barca's third goal? We have to watch the game back, but it won't change anything. There's a lot more of the league still to play, but we have to think about our next game."
Next up for Real Madrid, who still have a game in hand over Barcelona, is a trip to Deportivo La Coruna on Wednesday night.