Real Madrid 3 Galatasaray 0
Real Madrid: Ronaldo 9', Benzema 29', Higuain 73'
The Bernaneu side took a huge step towards a third consecutive appearance in the semi-finals after Cristiano Ronaldo, Karim Benzema and Gonzalo Higuain gave the home side a comfortable advantage to take to Istanbul next week.
Yet despite the margin of their victory, Mourinho insists the club cannot afford to take the second leg lightly.
"They need a miracle but miracles happen in football, the history of football is full of miracles, why can they not dream of a miracle?" he said after the match..
"They will give their all to try to pull off a historic result and I have enough experience to know that although I am happy with the result, the tie is not over. I have to convince my players to believe that too."
"The team played well and produced a professional and balanced performance.
"We defended well and were dangerous on the counter-attack. They knew that at this stage of this competition that matches are decided by the slightest of margins, and we were concentrated and played with humility."
Ronaldo got the hosts off to the perfect start as he calmly chipped home from Mesut Ozil's wonderful through ball after just nine minutes.
The German international received Xabi Alonso's pass before turning and feeding Ronaldo to dink the ball over the advancing Fernando Muslera for his ninth goal of the competition.
Didier Drogba nearly produced an immediate reply for the visitors as he spun Raphael Varane on the edge of the box, but with a clear sight of goal the Ivorian lashed wildly wide of the target.
He then hit the target with another long-range strike that Diego Lopez could only turn behind for a corner. Galatasaray had a good claim for a penalty turned down when Sami Khedira appeared to handle inside his own area.
Yet, they were still struggling to cope at the back and went further behind when Michael Essien's cross just evaded Ronaldo but fell perfectly for Benzema to slot in off the near post.
Emmanuel Eboue had a great chance to give Fatih Terim's men a lifeline just before half-time, as he broke through on goal after a neat exchange of passes with Drogba, but the former Arsenal defender fired his shot too close to Lopez, who made a comfortable save.
Galatasaray changed to a 5-3-2 formation in the second half, with Wesley Sneijder replaced by Gokhan Zan, but could not stem the tide of Madrid attacks, and the game was all but killed off 17 minutes from time though as substitute Higuain glanced home Alonso's in-swinging free kick.
Afterwards Terim criticised referee Svein Oddvar Moen's performance, above all his decision to book striker Burak Yilmaz instead of awarding a penalty following a challenge from Sergio Ramos late on.
"Maybe the name Real Madrid affected Galatasaray and the referee did not have courage," Terim said.
"The referee made many mistakes. Burak was fouled, everyone saw it except for the referee, but despite everything there is nothing we can do, the result is there for everyone to see."
He also rued his side's carelessness in conceding Ronaldo and Benzema's goals, as well as pointing the finger at Drogba and Eboue for squandering goal scoring opportunities.
"At this level in these kind of matches you cannot make clear mistakes," he said.
"The first and the second goals were basic mistakes and then with Eboue and Drogba we couldn't take two clear chances. If we had taken advantage of those moments the match could have been different."
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