The English club clawed their way back into contention in the second spell with a try to former Springbok Thinus Delport, converted by Cook Islands international Tommy Hayes, but that was the end of the visitors' scoring and their European campaign has ended after only two matches.
Brive winger Julien Laharrague scored 25 of his side's points and they now play one of the two "lucky losers" in the second round of the Cup.
Elsewhere in France, Pau beat Gran Parma 31-22 to cruise into the second round. Winger Rida Jaouher scored a try double and fullback Julian O'Neil converted three of his side's five tries, and Pau play the winners of today's London Irish-Auch match in the next round.
Agen romped to a 59-21 win over L'Aquila and they play Viadana in the second round after the Italian club hammered Spanish amateurs VRAC Rugby 59-7. Viadana fullback and former England winger Tom Beim scored two tries and was named man of the match in a one-sided contest.
Clermont Auvergne backrower Elvis Vermeulen scored a hat-trick of tries as his side crushed Italian battlers Leonessa 51-6 and they play Scottish province Borders in the next round.
In earlier games, Irish province Connacht continued their fine record in Europe by overturning a 14-point first-leg deficit against Narbonne to reach the second round.
Connacht went into the match at the Sportsground needing a 15-point victory after last weekend's 11-25 loss in France, and came up trumps with a convincing 40-21 win. Outside-half Paul Warwick was the hometown hero, scoring two tries and kicking a further 22 points in a superb individual performance.
In other matches, Beziers romped past Petrarca Rugby 69-18 to cruise into the second round with two victories. Winger Philippe Escalle bagged a hat-trick as Beziers ran in 10 tries at the Stade de la Mediterranee, and his side play a tough Grenoble outfit in the next round.
Italian club Overmach Parma sneaked into a second-round series against Saracens with a 36-10 victory over Spanish outfit El Salvador. Parma needed to overturn a first-leg 24-point deficit and managed it by a mere two points.
They were helped by Irish referee David Keane, who awarded two penalty tries in a hard-fought tussle. El Salvador lock Carlo Del Fava was red-carded for over-vigorous rucking and later suspended from all rugby for 10 weeks.