Garvey was cited by Leinster for allegedly stamping on outside-half Nathan Spooner in the Celtic League quarter-final in Dublin on November 30.
The WRU disciplinary committee upheld the citing and imposed the ban. Newport coach, McIntosh said: "In the end we have little or no option other than to accept the verdict, but I don't feel it is fair or warranted. There was no mention of stamping and, as far as I can see, there is no conclusive evidence on the video to suggest it was Adrian who caught Spooner. We go out to play hard, but fair rugby at Newport and we certainly do not condone foul play. I feel the whole incident was an accident."
Having established that Garvey, was going to be cited, Newport opted to cite two Leinster players, Trevor Brennan and Spooner himself, for high tackles. However neither citing was upheld by the disciplinary committee.