"They took an upbeat edgy song and turned it into a slow boring lame song," said another.
Others praised Coldplay for the tribute and their attempt at performing the song.
Yauch died on Friday after a three-year battle with throat cancer. He was 47.
Celebrities have honoured the rapper, including Madonna, who said he was one of a kind and the group was important to her musical history.
The singer says the seminal hip-hop group was "integral to the musical revolution that was happening at the time".
Madonna says she was sad to hear of Yauch's death and asked God to bless his family.
The Beastie Boys opened for Madonna on tour in the 1980s, and the group was inducted into the Rock and Roll Hall of Fame last month.
Watch Coldplay's cover of (You Gotta) Fight for Your Right (to Party!):
- Herald online with AP