Neville sent on Carney for her 144th and final England appearance 17 minutes from time, while Nilla Fischer's brilliant goal-line clearance prevented Lucy Bronze from taking the game into an additional period.
England were then relieved not to see further sloppiness at the back punished in first-half stoppage time as Blackstenius took the ball off Steph Houghton and lofted an effort on to the roof of the net, and White saw a strike kept out by the outstretched leg of Hedvig Lindahl.
Sweden survived a late England rally to secure third place, adding to the bronze medals they collected in 1991 and 2011.
Ellen White thought she had tied the score two minutes later but her goal was ruled out after the video review determined there had been a handball.
"In 2015 we won bronze with magnificent performances, a manager (Mark Sampson) and a set of players that were great, and we celebrated and applauded".
Within moments, it looked as if the Lionesses had scored again, White bringing down a Beth Mead delivery with her back to goal, holding off Linda Sembrandt as she turned and slotting the ball in.
The 30-year-old, level at the top of the scoring charts with United States star Alex Morgan, nearly equalised again on the stroke of half-time but shot straight at Swedish 'keeper Hedvig Lindahl. 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.
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.
She is the second-most capped player for England, behind only Fara Williams who has played 170 times for the Lionesses.
There have been five goals awarded and subsequently overturned by VAR at the 2019 Women's World Cup.
England boss Phil Neville did not pick Carney in his early squads after being appointed previous year, as she was injured.
But Phil Neville played down the importance of the game, labelling it "nonsense". The courage to keep going forward, the energy - the players gave everything.
Telford made a good near-post save to deny Jakobsson but was powerless to prevent the Montpellier winger from curling a shot into the far corner after England's defenders allowed her to dribble into the box unchallenged. "We have just got to make sure that next time we are better", Neville said on BBC One.
Tedy Bruschi "recovering well" after having a stroke
Bruschi, now 46, played for the Patriots his entire career, winning three Super Bowls before retiring after the 2008 season. The statement said Bruschi recognized his symptoms, arm weakness, face drooping and speech difficulties, immediately.
Joey Chestnut wins 12th hot dog eating title
Joey "Jaws" Chestnut and Miki Sudo clinched victory in the annual Nathan's Famous July Fourth hot dog eating contest Thursday. Chestnut threw out the first pitch at a New York Mets game on Sunday.