Zidane controversially instructed his players not to form a guard of honour for Barcelona prior to the match, setting the tone for an ill-tempered game which saw eight yellow cards, one red card for Sergi Roberto and a number of controversial refereeing decisions.
Barcelona ultimately held out with a numerical disadvantage for 45 minutes to earn a draw which keeps their hopes of an unbeaten season alive, and Zidane acknowledged that both teams contributed to a "great game".
"I would liked to have won. In a Clasico where there was nothing at stake, it was a great game. We both went out to play. We both played a great game and football is always the most important thing, more so than the controversies," he told reporters in his post-match press conference.
"It was a difficult match for the referee, but I'm not going to get involved, it's tough. There's been a bit of everything but that isn't going to change anything at the end. It is done.
"We played a good game [before the red card] and, in contrast, with the extra man we were a bit worse. We needed to have a little more patience, but that doesn't change anything. We must congratulate Barcelona."
Madrid, who still sit third in the table, have three league games remaining before facing Liverpool in the Champions League final on May 26.