Atalanta midfielder Remo Freuler was sent off for a professional foul on Ferland Mendy only 17 minutes into the first leg of the round of 16 tie at Gewiss Stadium on Wednesday.
A depleted Los Blancos side, who have the likes of Karim Benzema and Eden Hazard on a long list of absentees, lacked ideas and looked set to fire a blank prior to Mendy's sweetly struck late away goal.
Zidane knows Madrid's fifth consecutive win was not pretty, but he was relieved to take the upper hand heading into the second leg at home on March 16.
The Madrid head coach said: "We didn't play a great game tonight, but I think the most important thing is the result.