The 27-year-old left Tottenham Hotspur in August after a drawn-out saga that led to Real paying a fee of up to 42 million euros, according to media reports.
"This is a very technical league but also a very demanding one in physical terms," said Modric who has only started 11 games in La Liga.
"Little by little I am getting used to it. I don't like to give myself a mark out of 10 but I'm not entirely happy with my performances so far," he told a news conference.
"In some games I have shown why I was brought here but in others I haven't. I missed pre-season and this has had an influence.
"The coach and my colleagues have had a lot of patience with me. I think the club and the fans will end up being pleased with me."
Real, third behind Atletico Madrid, host Sevilla in La Liga on Saturday when they will try and make inroads on a 16-point deficit on leaders Barcelona.
One positive for coach Jose Mourinho, who has one eye on Wednesday's visit of Manchester United in a Champions League last-16 first leg, was the return to fitness of defender Pepe for the Sevilla game.
The Portugal centre-back, out since the turn of the year due to ankle surgery, has been included in Real's 19-man squad after having returned to training in the week.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.