The rookie coach vanquished the Italians at the Stadio Olimpico to continue his fine run after taking over from Rafa Benitez, and praised his scorer for breaking down the hosts
The Portugal international opened the scoring with a deflected effort that broke down Roma's resistance in the Italian capital, and Jese doubled the lead to give Real a 2-0 advantage from the first leg.
Speaking after the game, Zidane admitted he was over the moon with his forward's goal, which he dedicated to the coach.
"He had a brilliant match, but so did everyone, even those who did not play and cheered us on," he told Bein Sports at the final whistle.
"I am happy about his goal, but above all because he found the net."
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The Frenchman's Champions League debut on the bench ended in an encouraging victory, and he paid tribute to his team for coming through a tough away test.
"It was special, I am pleased with the result," he said.
"It was a tough match, we knew that. We fought until the end and we took away a big result.
"It is normal for the other team to pressure you, [Roma] played well in the first half.
"This is the Champions League, it is a tough competition."