Madrid progressed to the last 16 with a 4-2 aggregate win but Zidane's men were forced to dig deep against the unheralded visitors in the second-leg fixture at the Santiago Bernabeu on Tuesday.
Fuenlabrada took a deserved 25th-minute lead thanks to Luis Milla's stunner in the Spanish capital – where Gareth Bale returned from injury – before a quick-fire brace from Borja Mayoral in the second half allayed fears around the stadium.
Alvaro Portilla struck at the death to secure a memorable draw for Fuenlabrada but head coach Zidane, who named the youngest team of his Madrid reign, was upbeat post-match.
@Mayoral_Borja's brace secured our passage into the Copa del Rey last-16!
— Real Madrid C.F. (@realmadriden) November 28, 2017
"I'm not upset at all, it was foreseen," Zidane told reporters. "It's not easy for the players, there were homegrown players.
"I'm happy to advance in the tie, the opponent played a very good game. The important thing is the tie and we passed."
Zidane added: "People can say what they want, but they also saw their players fight until the end.
"There were players who had not played together. The opponent does not have a level of Segunda B. Fuenlabrada are a good team."
"I'm looking at my players, those who were on the field, in the second half we did it well, I'm happy," he continued.
Photo by: Getty Iamges. Caption: Real Madrid head coach Zinedine Zidane