The La Liga outfit had to wait until the 74th minute before Madrid striker Karim Benzema finally made the breakthrough against a resilient Apoel outfit.
Second-half substitute Kaká teed up the French striker for Madrid’s fist goal, and the former AC Milan midfielder doubled the visitors’ advantage before Benzema netted his second on the stroke of full-time.
“We won because we played well,” Mourinho said. “Defensively, Apoel did well and they always played with a good spirit.
“What they are doing this season is fantastic. We had to be at our best tonight in order to achieve this result.
“We had a lot of respect for our opponents tonight, the same respect we will show them at the Santiago Bernabéu – they are the most important team in this season’s Champions League.”
Meanwhile, Apoel manager Ivan Jovanović conceded Madrid deserved to win in Cyprus, but the 49-year-old described the chance to play Mourinho’s side as an “honour”.
“This year has been surreal. Our aim was first and foremost to enter the group stage,” said Jovanović.
“To get into the knockout phase ahead of Zenit, Porto and Shakhtar was a fantastic accomplishment, as was our being able to eliminate Lyon.
“Perhaps the fact that we got the chance to play Madrid was another gift. It was an honour to play against them.”
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