The Uruguayan international expressed a desire to leave the Merseyside outfit during the summer window, but following two rejected bids from Arsenal, the prolific striker remained at the club.
While admitting that captain Steven Gerrard gave him "advice" about his future, the 26-year-old has also stated that the fans played a role.
"The support of the fans was also very important," Suarez told Sport 890. "I always could walk on the street with no trouble. I was never threatened or anything like that, it was all made up. The people told me to stay. I work hard for Liverpool and I will always be thankful to the club."
Despite staying at the club, Suarez has been linked with a January move to Real Madrid.