Argentina had already wrapped up their fourth-straight title at the four-team tournament with wins against second-place United States and Uruguay.
The Americans moved into second with a 20-8 win over Uruguay earlier Saturday.
Conor Trainor and Mike Scholz scored for Canada (1-2) but two successfully converted tries by Argentina while Canada was down to 14 men in the first half was the difference.
Canada's coach Kieran Crowley was content with his team's performance if not the result.
"Very pleased with our effort from the guys tonight, I thought we really stepped it up. We showed a little bit of what we could do, which was lacking in the first two games," said Crowley.
Sebastian Poet kicked off the scoring early in the game with a penalty goal to give Argentina an early 3-0 edge.
Canada regained momentum thanks to Scholz, who burst into the try zone just moments later for a 7-3 edge after Jack Fitzpatrick successfully made his first conversion attempt of the night.
With Canada down to 14 men toward the end of the second half, Argentina seized the opportunity and scored two tries in a matter of minutes to put the score at 17-7.
Canada received a boost in the 66th minute from Trainor. While Argentina was harmlessly passing the ball across the field, Trainor stepped in and picked off a pass intended for an Argentinean player.
With nothing but the posts to stop him, Trainor dove into the try zone and cut the lead to just three points following the third successful kick in as many attempts for Fitzpatrick.
Canada kept up the intensity for the remaining time, coming close to scoring the game-winning try on several occasions.
Penalties hampered Canada's ability to advance the ball toward the closing moments of the game and Argentina's Patricio Fernandez made two consecutive penalty goals to increase their lead to nine and put the game out of reach.