Kieron Darlow, 25, made the gestures at the match between Liverpool and Tottenham at Anfield on April 30th, the Crown Prosecution Service (CPS) said, where his actions were reported to police and he was identified and arrested.
"Darlow, a Tottenham fan, admitted making a gesture towards Liverpool fans and that this was a reference to the Hillsborough disaster," said Andrew Page, associate prosecutor at CPS Mersey Cheshire.
"He admitted that the gesture suggested that the ticketless fans had been pushed forward in the tragedy and had been partly to blame for the crush that led to so many deaths.
"He accepted in court that it was his intention that Liverpool fans should see this and that it would cause them harassment, alarm and distress. That kind of behaviour is not just morally unacceptable, it is criminal."
Darlow was handed an order at the North Liverpool Community Justice Centre banning him from football matches and the vicinity of stadiums for three years.
"We hope this prosecution sends a message to all football fans that their behaviour at football matches is important and that if it becomes criminal they will be punished to the full force of the law," Page added.
The 1989 FA Cup semi-final was the scene of Britain's worst sporting disaster and resulted in 97 Liverpool fans losing their lives after a clash in an overcrowded and fenced-off ground.
Earlier in April, Liverpool had called for an end to "vile chants" over Hillsborough after they were heard during their goalless Premier League draw with Chelsea at Stamford Bridge.
