The midfielder was booed by some visiting fans when he came off the bench during Sunday's 2-2 draw at Anfield to a rousing welcome from Liverpool supporters.
Benayoun previously played for Liverpool but claims his recent cool reception from a section of the Chelsea support is down to a recent interview he gave in defence of Fernando Torres.
The Israel international, who is out of contract this summer, wrote on his Twitter page: "The booing came from some small part of the Chelsea fans that have been doing it in the last few weeks since I did an interview about Torres.
"But I don't really bother about it... people need to understand what they read.
"There are some other issues that the club is trying to handle in the right way... as sometimes people are crossing the limit and I'm sure the club will sort it.
"What's important for me is to do the best for the team till the end of the season, try to finish in the top three and win the Europa League... and then look for my next challenge."
Benayoun said in a February interview Torres' confidence was damaged when he was in and out of the side at the beginning of his Chelsea career.