The Frenchman admitted that Los Blancos did not have an easy game in Cyprus, but was over the moon with the final result in Tuesday's Champions League encounter
Jose Mourinho's men were unable to breach the APOEL defence in the opening 45 minutes, but eventually broke the deadlock in the 74th minute when Kaka set up Benzema for the opener, before the pair added two more in the closing stages of the match to record a 3-0 away win.
"It was a very difficult game, especially in the first half. The game improved after half-time and we earned a very important victory. We will keep it up in the return leg," Benzema was quoted as saying on the official Madrid website.
"APOEL are a very tough opponent and made things hard for us. This is an important victory, but this isn't over yet. We want to give a good performance before our fans in the return leg.
"I had a very good chance to score before I netted my first, but I tallied two in the end and that's what matters. We did very well and took a major step towards winning the tie."
The second leg takes place at the Santiago Bernabeu on April 4.
For the next 10 weeks, Goal.com will be publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. Check out the first extract, published on Friday, which looks at the Portuguese forward's humble beginnings in Madeira. Don't miss it!