Montreal's Auger-Aliassime and Ottawa's Dabrowski were defeated 6-3, 6-4 by the second-seeded Greek tandem of Stefanos Tsitsipas and Maria Sakkari.
Auger-Aliassime and Dabrowski had a more accurate service game than the Greek team, particularly on second serve.
But the Canadians failed to take advantage of chances to take momentum in the match. Auger-Aliassime and Dabrowski couldn't convert any of the four break-point chances they had.
Tsitsipas and Sakkari made good on two of their six break-point opportunities.
The Greeks had six aces, two more than the Canadians.
While Dabrowski has two Grand Slam mixed doubles titles to her name, the discipline is new to Auger-Aliassime.
Canada's tennis team managed to win just one match in Tokyo, with Leylah Fernandez winning her women's singles opener before falling in the second round.
Auger-Aliassime was defeated in the first round of men's competition, as was the women's doubles team of Dabrowski and Sharon Fichman.
Coming home empty-handed will be disappointing for a country that is fast becoming a tennis powerhouse.
However, Canada's team was hurt well before the Games started when its two top players, Bianca Andreescu and Denis Shapovalov, decided against going to Tokyo. Vasek Pospisil, originally slated to play men's doubles with Auger-Aliassime, later followed suit.
The Greek duo will now face Ash Barty and John Peers from Australia.