But he stressed that, despite the elimination of a host of big names from the tournament in Russia, England would be taking nothing for granted.
"We owe the fans a lot of thanks as well for the way they have supported us".
"That's so important for us on Saturday because I always think Sweden like to point out we're paid this and that, and we're the team of entitlement, when I don't think that is the case for this group".
Sweden were undone at two set pieces - goals from which are becoming quite a trend for England - but the Swedish manager lavished praise on England for being "the best team".
Before England's second goal Sweden missed a golden opportunity to level right after the restart but Pickford, who was named man of the match, made an outstanding save, palming Marcus Berg's close-range header away.
But Maguire claims it was down to the players feeling so comfortable against Sweden.More news: 11 bodies recovered at a house in Delhi’s Burari
Gareth Southgate's understandably very proud of his players!
"But that's something we'll work on and take to the next game".
They lacked the resilience displayed in the last-16 defeat of Switzerland, but Andersson said the outcome was through England's excellence more than anything. Congratulations to both the team and the coach.
"Personally, I don't think I played as well as I should have", he said.
England forward Raheem Sterling has yet to score at the World Cup from his unusual position as the support striker to Kane, and his finishing let him down against Sweden. He is likely to retain his starting place for the semifinals.
Sweden had reached the quarter-finals by making life hard for supposedly superior opponents and it was easy to see why after a dour opening when England looked incapable of stringing passes together against their hardworking opponents.
It's been a long time between drinks for England football fans.
One report suggests that Germany fans had bought tickets to the game anticipating that they would be the side getting through to the match.