Kieron Darlow, a 25-year-old man from Welwyn, north of London, made the gestures at a game between the teams at Anfield on April 30, British prosecutors said.
“Darlow was laughing and those who challenged him said he caused real alarm and distress,” the Crown Prosecution Service said.
Darlow’s ban also prevents him from being in the vicinity of stadiums.
“Darlow admitted making a gesture towards the Liverpool fans and that this was a reference to the Hillsborough disaster,” prosecutor Andrew Page said. “He admitted that this was to suggest that fans without tickets had pushed forward in the tragedy and had been partly to blame for the crush that led to so many deaths.
“He accepted at court that it was his intention that Liverpool fans should see this and that it would cause them harassment, alarm and distress. He admitted that his behavior was unacceptable and regrets his actions.”
Ninety-seven Liverpool fans died as a result of a crush at Hillsborough in 1989, making it Britain’s worst sporting disaster.
A jury at an inquest ruled in 2016 that the fans were unlawfully killed amid a number of police errors.