The 33-year-old forward was docked the equivalent of six match fees by the club's disciplinary committee following Saturday's stamping incident in the Courage League One game at Northampton.
The referee, Jerry Wallis, on the advice of his senior touchjudge, Geraint Ashton Jones, sent off the Bristol No 8, Eben Rollitt, over the incident.
However, both officials have admitted that the wrong player was shown the red card and apologised for their mistake, after viewing video evidence.
Bristol's disciplinary committee - consisting of the chairman, Derek Brown, the coach, Alan Davies, and the captain, Martin Corry - viewed that evidence as well and interviewed Adams before announcing their judgment.
"The player admitted that he had committed the offence but stressed that it was not intentional and would like to apologise to all, especially the Northampton player involved," Brown said.
The club will be informing the Rugby Football Union and Northampton of their action and hope that this will conclude the matter.
In March 1990 Adams was sent off by the former international referee Laurie Prideaux for kicking the second row Colin Pinnegar in Bristol's 22-21 home defeat by Wasps. Adams then faced a Gloucestershire county disciplinary committee and was banned for a club record of 75 days.
Adams, who has been with Bristol for 11 seasons, said: "I think I had a very fair hearing and accept the decision of the disciplinary committee.
"I would like to apologise for the incident which was in the heat of the moment, but acknowledge that it should not have taken place. I now wish to put the matter behind me."
The power of Saracens has proved to much for the rugby league club Oldham Bears, who have abandoned attempts to sign Halifax's former Great Britain centre, Graeme Hallas.
"We put a good deal to him but we can't match the money on offer in rugby union," the Oldham coach, Andy Goodway, admitted. Oldham received Halifax's permission to approach Hallas, who looks to be heading for the union club when his contract at Thrum Hall expires on 31 December.Reuse content