The midfielder's career at Real stalled in the summer due to injury problems, but he featured in victory over Getafe.
"They've really welcomed me and it was a shame that I got injured my first week here. But I'm constantly improving and we'll see if little by little I can get into top form," said Illarramendi.
"The season is long and there will be games for everyone. I have to enjoy the game and the minutes I have."