Already leading 3-0 from the first-leg the hosts started brightly but had to wait until the 25th minute to open the scoring as Cristiano Ronaldo tapped home Marcelo's cross at the back post.
Kaka doubled Real's lead with a stunning effort from outside the area nine minutes before half-time, but the goal of the night was arguably scored by Gustavo Manduca as he pulled one back for the visitors after a flowing team move midway through the second-half.
Ronaldo soon restored the hosts' two-goal advantage and substitutes Jose Maria Callejon and Angel Di Maria added further goals either side of Esteban Solari's 82nd-minute penalty for the visitors.
Mourinho said: "We knew it was almost impossible for APOEL to win 4-1 so it was not easy to motivate the boys when we had it under control.
"But we did our job and I could use the game to get players miles in their legs."