The Canadian men opened the day with a 21-10 win over Kenya before losing 38-19 to France in the consolation Bowl semifinals.
Fiji won the tournament title later Sunday, routing defending champion New Zealand 33-19 in the final. South Africa finished third, beating Samoa 26-5. The U.S. Eagles were fifth.
Drawn in a tough pool Canada went 1-2 in the first two days of competition, with a victory over unheralded Belgium and losses to Samoa (24-19) and Fiji (45-0).
On Sunday, Harry Jones, John Moonlight and Sean White scored tries for Canada against Kenya with Jones kicking three conversions. Liam Underwood, who eventually left with an injury, scored two tries and Pat Kay added another with two conversions from Jones in the loss to France.
The win was Fiji's third in four years in the Hong Kong Sevens, and a record-extending 13th in the tournament.
Fiji's third win from six tournaments in the sevens world series also lifted it above New Zealand into second place, two points behind leader South Africa, and in position to win a first series in nine years. New Zealand, overall champion last season, is one point behind.
Canada remains in 13th place
The Japan Sevens is next weekend in Tokyo. Canada is will play in a pool with Kenya, South Africa and the U.S.
Fiji raced to a 21-0 lead in the first half of the final, taking the tension out of the 12th final matchup between the tournament's most successful sides.
Each time New Zealand rallied, Fiji had a reply, and even denied New Zealand the last say when Fiji's Vatemo Ravouvou and Apisai Domolailai bundled out Rieko Ioane just shy of the left corner flag.
"Tactically, we were really astute," Fiji coach Ben Ryan said. "I'm really pleased with the way they managed the final."
Fiji did well merely to survive its quarter-final. It led England 14-5 with a penalty try, then lost a man to the sin-bin, too. England, at 14-12 down, gave James Rodwell a chance in the right corner, but Rawaca pulled off a brilliant try-saving tackle.
Fiji blasted to a 21-0 lead against South Africa in the semifinals then just managed to hold on 21-15 in another thriller.
"That's a great Fijian side," New Zealand coach Gordon Tietjens said. "They defended really well and a couple of length-of-the-field tries killed us."
— With files from The Associated Press.