White's frustration at the decision was clear, but that was shared by her team-mates at the full-time whistle as they failed to draw level despite dominating the second half, Lucy Bronze seeing a late strike cleared off the line by Nilla Fischer.
England regrouped and after half an hour they halved the deficit when Kirby dribbled from the right into the penalty area, cut on to her left and curled the ball in off the far post.
It was a second defeat in under a week for Phil Neville's Lionesses, after suffering their third straight major tournament semi-final loss when beaten 2-1 by reigning champions the United States on Tuesday.
It was a third bronze medal for Sweden, which also finished as the runner-up in 2003.
Karen Carney's glittering career will come to an end after England's World Cup play-off on Saturday.
Within moments, it looked as if the Lionesses had scored again, Ellen White bringing down a Mead delivery with her back to goal, holding off Linda Sembrant as she turned and slotting the ball in. England won it in 2015, and Sweden did the same in 2011.
But there was a subsequent VAR check for handball and, after watching footage back pitchside, referee Anastasia Pustovoytova ruled the effort should not stand.
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White was then denied in first half injury time when through one-on-one with the Swedish keeper with Hedvig Lindahl expertly smothering her effort.
Neville sent on Karen Carney with 16 minutes remaining for her final appearance before retirement, and the 31-year-old immediately helped England get onto the front foot. Meanwhile, this young Sweden team may just be viewed as a favorite at the 2023 World Cup with 15 of its 23 players age 26 or younger and having put together an impressive run at this year's tournament.
Sweden, who lost to Netherlands after extra time in the semifinals, begun the brighter of the two teams and profited from some slack England defending to take the lead on 11 minutes.
She is the second-most capped player for England, behind only Fara Williams who has played 170 times for the Lionesses.
But Phil Neville played down the importance of the game, labelling it "nonsense".
"To give an example of what kind of professional Karen is. we have the option of some players going to training early. The two goals sparked us into life and I don't think I have seen us play better than we did after those first 20 minutes", Neville added.
"I feel incredibly honoured that I, in a short space of time, got to know one of our greatest players, but more importantly, what an unbelievable person, and that makes me a lucky, lucky manager", said England coach Phil Neville.