The Canadians had needed a win to advance to the knockout round of 16.
"You have to take care of your own business and get your own results." said coach Sean Fleming. "At the same time, it seemed like every result that could have helped us didn't go our way."
The loss, which dropped Canada's career record to 0-14-4 in six editions of the youth tournament, followed earlier Canadian ties with Iran (1-1) and Austria (2-2).
Canada played its three games in nine days.
Joaquin Ibanez scored in first-half stoppage time and Matias Sanchez scored in the 46th minute for Argentina. Sanchez made it 3-0 in the 75th minute.
Argentina (2-0-1) won Group E with seven points. Iran (1-0-2) also advanced after defeating Austria 1-0 to finish runner-up in the group with five points.
Canada (0-1-2) placed third with two points while Austria (0-2-1) was fourth with one.
For our football in Canada, we may not always be known for our attacking qualities, but I think this team does have good attacking players," .
"I think highlights for this group has to include our resiliency to come back in games. We had to do that in CONCACAF and we had to do that here," said Fleming. "To see that character in the kids is great.
"We also scored some great goals in the last 14-15 months that we were together. Those were highlights, too. Really, just to see the improvements overall as a group and individually amongst our footballers was a highlight."
The top two teams in each of the six preliminary-round groups advance, along with the fourth third-best teams.
The five other third-place teams all had more points than Canada.
The young Canadians have never made it out of the first round at the world championship at this level and its two draws at the 2011 event in Mexico represented their first ever points at the competition.
The points won have all come under Fleming as coach.