The Lionesses were seeking to claim a second successive World Cup bronze medal but were rocked by two early goals from Kosovare Asllani and Sofia Jakobsson.
Fran Kirby’s strike on the half hour narrowed the deficit and City striker Ellen White then thought she had levelled but, just as in the Lionesses’ semi-final loss to the United States last Tuesday, her strike was ruled out by VAR.
And despite a fine second half showing England couldn’t crack open the Swedish back-line as the Lionesses’ memorable exploits in France ended in frustrating fashion.
Manager Phil Neville made four changes from the side which lost out 2-1 to the Americans with City trio, skipper Steph Houghton, midfielder Jill Scott and striker Ellen White all starting.
England went into their first-ever World Cup meeting with Sweden knowing their record against the Scandinavians left a lot to be desired, the Lionesses having registered just three wins from 26 previous clashes.
And the Swedes, who lost their own semi-final 1-0 to Holland on Wednesday, began on the front-foot with their early pressure and dominance rewarded by an opening goal on 11 minutes with England architects of their own downfall.
With England down to 10 players while Houghton was waiting to come back on the field after an ear problem, Fridolina Rolfo fired in a seemingly innocuous cross in from the left.
Alex Greenwood had time to clear but instead she fired the ball straight into the path of former City striker Asllani.
The Swedish striker gratefully accepted the invitation, hitting a sweetly-struck shot which found the bottom right hand corner of the net despite goalkeeper Carly Telford getting a hand to the ball.
The Swedes so nearly struck again on 17 minutes. A ball over the top of England left channel found the unmarked Jakobsson with the time and space to shoot
Fortunately for the Lionesses her strike hit the post and then struck Telford before going out for a corner.
However, the dominant Swedes didn’t have to wait too long to double their advantage.
On 22 minutes, the impressive Jakobsson again exploited gaps in the England back line, this time on the right and then curled home a superb shot past Telford.
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England needed a response and it arrived on the half hour. Scott was the architect feeding a wonderful pass through to Fran Kirby, who cut in from the right before dispatching the ball home.
Within two minutes it looked as the Lionesses had drawn level through White only for VAR to dash her hopes once again.
The City star cushioned a ball from Beth Mead before firing home for what she thought was her seventh goal of the tournament.
However, for the second game in a row White had a goal chalked out by VAR with a subsequent check by the officials ruling that she had handled the ball in the build-up to scoring.
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.
England maintained their dominance in both possession and territory after the break but were frustrated with their final ball though Jodie Taylor, the impressive Fran Kirby and Scott all threatened.
The introduction of substitute Karen Carney – winning her 144th cap on her final appearance in football after an illustrious career – further invigorated England and her 78th minute burst down the left flank almost saw White level.
And 90 seconds from time Lucy Bronze powered in a superb volley from Greenwood’s corner only for Swedish centre-half Nilla Fischer to head the effort off the line.
It means England go home empty-handed but having inspired a nation with their efforts during a memorable past month.