The Portuguese tactician hailed his team's efforts and highlighted the fact they have started their league campaign brighter than last year
The Spanish capital club got off to a flying start in La Liga as a hat-trick from Cristiano Ronaldo, coupled with goals from Marcelo, Xabi Alonso and Kaka gave them a convincing win in their league opener.
Mourinho admitted that Zaragoza could not field their best line-up due to injuries, but was pleased with Madrid's resounding win.
"In order to win, you have to play well. At least, that is what happens at Madrid. If we won with this scoreline, it was because we had a very good match," he told the media after the match.
"I will not hide the fact that the Zaragoza coach had several difficulties. Players like Mateo, Juan Carlos, Braulio and Ruben Micael are all very good and were not here tonight.
"We played seriously and with ambition until the last minute, and that is the reason for this scoreline."
After Real Madrid were held to a goalless draw in their league opener against Mallorca last season, Mourinho was happy that his side fared better this time around.
He added: "The important thing is that we won, because last year we had one point after the first matchday, and now we have three."