The Lionesses lost 2-1 in Lyon, with Ellen White having a goal ruled out by the VAR for offside and captain Steph Houghton having a late penalty saved.
‘I’ve told them no tears tonight,’ said manager Phil Neville.
‘I’m proud. They have touched the hearts of the nation, I couldn’t ask for more. We had the time of our lives.’
England must now shrug off the heartbreak of a third consecutive semi-final defeat in a major tournament to face either Sweden or the Netherlands in Saturday’s third-place play-off.
‘We only had a 10-minute period in the first half where we played with the belief that we talked about. We stood off them too much. We will learn massively from this.’
Neville accepted the offside decision against White was correct but said Bright should not have been shown her first yellow card and he thought ‘the referee wasn’t really in control of the game’.