The former Liverpool midfielder says he is comfortable with his role at the club and believes he is gradually improving.
“I believe that I have an important role and I am happy, but I have just arrived and am still adapting,” he told the official club website.
“I am improving slowly, just like the team. I am getting more comfortable.
“The team is attacking and defending better, and we are more balanced. I also do the “dirty work” sometimes.
The Spaniard also had praise for fellow team-mate Lassana Diarra, who moved to Madrid from Portsmouth at the end of 2008.
“Lass knows how to play with the ball very well. We combine very well.”
Real Madrid currently sit five points behind La Liga leaders Barcelona and face Malaga, who are unbeaten in nine games, at the Bernabeu on Sunday.
“It is important to be strong at home, and know that any visiting team is going to have to work very hard to get anything,” Alonso continued.
“We have had some good moments away from home, but we can probably improve a little.”
“[Malaga] are in good form, they have not lost in nine games, and that means they are doing well.”
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