Alonso made his first appearance of the season as a substitute in Wednesday's 7-3 triumph over Sevilla, following a five-month lay-off with groin and foot injuries, and could return to the starting line-up when Madrid face Rayo Vallecano on Saturday.
Illarramendi has deputised in the absence of the Spain international, but acknowledges Real are a better team with Alonso fit.
"He is important for us; he has been here for a long time and has always been important," said Illarramendi.
"There will be more competition and that is good for the team and helps us all to improve. We have a match every three days and we will have to rotate to get rest.
"The important thing is carry on as we are whoever plays."
Only Granada have mustered a lower tally than Rayo's eight and Paco Jemez's side have also conceded 27, more than anyone in the division.
