Best was suspended last Wednesday after admitting he had "made contact with the eye or eye area" of Wasps flanker James Haskell during Saints' 24-20 victory at Franklin's Gardens.
It was only Best's third game for the club following his summer move from Ulster.
The RFU panel accepted Best had not intentionally searched for Haskell's eye.
But they did not agree with Best's account that contact with Haskell's eye had been "fleeting" and described his actions as "grave".
Northampton decided to challenge the ban after taking legal advice but the RFU appeal panel threw out their case at a London hearing on Monday evening.