Asllani, who was taken off the field in a stretcher during Sweden's semifinal loss to the Netherlands, started Saturday and gave the Swedes the lead in the 11th minute as they took advantage of early struggles by England. Alex Greenwood had plenty of time to clear Fridolina Rolfo's cross but sent it straight into the path of Asllani, who drilled it into the bottom right corner. England goalkeeper Carly Telford got a hand to it but couldn't keep it out of the net.
Sweden almost doubled its lead five minutes later but Jakobsson's effort came off the right post and went out off of Telford's knee.
Jakobsson did score shortly after as she cut inside the left side before curling into the opposite side of the net.
England cut Sweden's lead to 2-1 in the 31st when Fran Kirby cut in from the right, beat her defender and fired one inside the left post.
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. The forward had also had what would have been an equalizing goal ruled out in the semifinal loss to the United States.
Lucy Bronze almost leveled in the final minute but her effort was headed off the line by Nilla Fischer.