The Spain international scored his team's third goal but humbly explains that his strike is not as important as their overall performance at La Romareda
Cristiano Ronaldo scored a hat-trick and Marcelo as well as Kaka netted a goal each, while 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 and stated: "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.