The 33-year-old has been suspended until 19 December following a stamping incident during Bristol's Courage League defeat at Northampton last month.
Adams was not sent off at the time as the referee, Jerry Wallis, mistakenly dismissed his team-mate Eben Rollitt, although he later apologised, but a three-man Rugby Football Union disciplinary panel used video evidence to help reach its verdict.
Bristol have already fined Adams an undisclosed four-figure sum for stamping on the Northampton lock, Jon Phillips, in a league game at Franklins Gardens last month.
However, in a statement, the club said: "We are disappointed by the sentence imposed on Mr Adams by the RFU special disciplinary committee hearing. The club had felt that the issue had been dealt with to the satisfaction of all concerned. The rugby club reserves its position on whether it will appeal against the sentence."
Adams, who was not cited for the offence, has 14 days in which to lodge an appeal against the suspension.
This is the second time in his 11-year career with Bristol that he has been banned, as he served 75 days for kicking a Wasps player in 1990.Reuse content