The Spain international scored his team's third goal but explains that his strike is not as important as their overall performance in the emphatic win at La Romareda
Cristiano Ronaldo scored a hat-trick, Marcelo and Kaka netted a goal each, and Alonso also added his name to the scoresheet in the 64th minute at La Romareda on Sunday evening when he drilled home a low shot from 25 yards out.
It was a dominating display from Jose Mourinho's men and the Spain international is delighted to have begun the 2011-12 campaign on a positive note.
"We did what we had to do," the 29-year-old is quoted as saying by Madrid's official website. "It's been a good start.
"The team was excited about starting the season and we're very happy."
Alonso, though, played down his contribution to Madrid's victory, stating: "I try to do my best for the team. I scored, but what matters is we won.
"It [my goal] helped because it came at the start of the second half and allowed us to relax a bit."
Madrid's arch-rivals and defending Spanish champions Barcelona begin their league campaign on Monday evening when they welcome Villarreal to Camp Nou.