The English pairing were edged out by Chinese duo Huang Kaixiang and Zheng Siwei 29-27, 21-8.
Defeat denied Briggs and Wolfenden a semi-final clash against Manu Attri and B Sumeeth Reddy, India’s top seeds who had beaten the Britons in the group phase.
The Indians had just shaded a tightly-contested, 68-minute match in the pair’s group match on Thursday.
Graham Hurrell, Badminton England coach, said: “We had to play a young Chinese pair in the quarters, one of whom had recently won the world junior championships in men’s doubles and mixed.
“It was an extremely close battle in the first set, neither pair could get more the two points ahead. Tom and Pete brought the best level using their height, with great angles and interceptions.
“In the second set the Chinese came out very fast and unfortunately took a very commanding lead, which was just too much to get back.
“Overall Tom and Pete have had valuable experience playing in this event, playing the round robin format, playing in a large arena with air conditioning and playing against two world class pairs.”
Briggs and Wolfenden, who now head to the US International in Orlando, were the only English players competing in Rio de Janeiro, with the Brasil Open acting as a test event ahead of next year’s Olympic Games.
Nonetheless, Briggs and Wolfenden will have given Jon Austin, Badminton England’s performance director, important insight into court and arena conditions for those players who qualify for the Rio Games.
Next week, Jon will also be offering his fact-finding thoughts on the Rio venue and how preparations are going for the 2016 Games.