Sweden raced into a 2-0 lead at the Allianz Riviera, with Kosovare Asllani firing in in the 11th minute after an Alex Greenwood error and Sofia Jakobsson adding a fine strike just 11 minutes later.
Phil Neville’s Lionesses replied through Fran Kirby’s effort just after the half-hour mark.
The ball was in the Sweden net again just two minutes later through Ellen White, however the goal was ruled out with VAR adjudging there to be a handball.
White’s frustration at the decision was clear, and it ended up a disappointing outing overall England.
That was despite the Lionesses, who had been beaten by USA in the semi-final, having much the the better of the second half.
Lucy Bronze came closest to forcing extra-time as she saw a late strike cleared off the line by Nilla Fischer.
Victory would have made the campaign in France England’s joint-best performance at a Women’s World Cup, four years on from them securing bronze for the first time in Canada.
Instead they must settle for fourth, while Sweden, the 2003 runners-up, take home bronze for a third time.
England boss Phil Neville said: “I think maybe there was carry on from the semi-final – the emotion.
“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.
“We gave it our best shot, we fell short and we just have to make sure next time we are better.
“Well done to Sweden but it is a nonsense game.