The City forward saw her well-struck spot-kick superbly saved by Hedvig Lindahl on 69 minutes after VAR had awarded a handball against former City player Kosovare Asllani.
Canada largely dominating proceedings, the Canadians created little of note on the night and were foiled by a goal from Stina Blackstenius on 58 minutes.
Beckie was lively and busy throughout, but Canada lacked punch in the final third and the penalty miss proved crucial in what was a tightly fought encounter.
Beckie was replaced on 84 minutes, ending a productive but ultimately disappointing tournament for the City star.
Asllani impressed for the Swedes and came close to extending their lead on a number of occasions.
Canada huffed and puffed to the end and even had a VAR check for handball as the Swedes celebrated, but the decision was no penalty and Sweden will now face Germany in the quarterfinal.