He was found guilty of using obscene, inappropriate and/or unprofessional language and behaviour towards fourth official Stuart Terheege.
Leicester beat Northampton 37-17 to secure a record 10th English title.
The former England hooker had pleaded not guilty to the charges at the hearing held in Coventry.
At half-time in the final at Twickenham, Northampton assistant coach Dorian West told ESPN that he felt Cockerill had been "intimidating" match officials.
Leicester Tigers say they will not be commenting on the matter until they have studied the RFU report.
Cockerill has been in trouble with the RFU before.
He was handed a four-week match-day ban for abusing officials during an LV= Cup tie with Newport Gwent Dragons in November 2009.
Along with coach Matt O'Connor he was accused of using foul or abusive language about referee Wayne Barnes during Leicester's Premiership semi-final defeat of Northampton in May 2011, although the RFU decided not to take any action.
He also received a formal warning from the RFU about his conduct after he took his frustration out on the wall of the coaches' box during a win over Bath on 16 May 2010.
Former hooker Cockerill played 27 times for England between 1997 and 1999, including four games at the 1999 World Cup.
Northampton skipper Dylan Hartley was sent off for abusive language just before half-time in the final, costing him his place on the Lions tour of Australia.
Leicester Tigers boss Richard Cockerill has been suspended for nine matches by the Rugby Football Union over his conduct in the Premiership final.