The 27-year-old joined the defending Spanish champions from Tottenham Hotspur last summer for £33million, but has failed to live up to expectations at the Santiago Bernabeu.
Having started just eight league matches so far this campaign, Modric was voted as the worst signing of the season in a poll on Marca's website.
However, the Croatia international is confident that he will regain his form for the second half of the season.
"This is Real Madrid and I know about the pressure from the media that surrounds all new signings," Modric told Sportske.
"I am not looking to make excuses because I am not that sort of a person, but it is a real challenge to adapt to a great club like Real Madrid.
"There have been some good performances, not in every game, but in general I feel that I have showed that I can offer something."