Germany’s Florian Wirtz scored a late equaliser in normal time to cancel out Dani Olmo’s 51st-minute opener and take the match in Stuttgart to extra time.
Penalties were beckoning when Spain scored a 119th-minute winner through Mikel Merino, Germany eliminated from their home tournament in heartbreaking circumstances.
‘Congratulations to Spain for reaching the semi-finals,’ Nagelsmann said at his post-match press conference.
‘The game was too open in the first half. We were better in the second half and from the 60th minute onwards, we were clearly the better team.
‘Our late [equaliser] was well-deserved. We conceded the winner with the last chance. Unfortunately we weren’t able to apply enough pressure on the wing.’
Asked what he said to his players in the dressing room, Nagelsmann added: ‘I told them that they don’t deserve [to exit the competition].
‘We’re all missing our families, but none of us wanted to leave. From the beginning of these last six weeks there’s been a very good atmosphere in the group. You could tell we gave everything to win this game.
‘Every player, whether they started or were on the bench, gave everything they had to win the game. It’s a painful one.’
Germany’s defeat to Spain was legendary midfielder Toni Kroos’ final game, the 34-year-old retiring having won multiple titles in Germany and Spain and lifting the World Cup with his country.
‘It’s impossible to over-appreciate Toni’s career,’ Nagelsmann said. ‘It’s probably unique for a German player.
‘He’s certainly one of Germany’s biggest players. Everyone knows about his success but not everyone knows about his character.
‘He spoke to the team in a very difficult moment for him personally. He always sees himself as part of this group.’
Spain boss Luis de la Fuente, meanwhile, hailed his team after they withstood a German fightback to book their place in the semi-finals.
‘This is the moment to appreciate what we’ve achieved and enjoy this moment,’ he said. ‘Physically we’ll see how we can improve in the next few days.
‘I’m sure that all of my players are ready [for the semi-final]. They’re playing at a very high level.
‘My players are insatiable. I’m proud to coach players like this. I’ve known many of them for many years. They’re used to competing at the highest level and they have an opportunity to win [the tournament].
‘This team are always going to compete. There’s always room for improvement, of course, but we can’t question their pride, quality and commitment.’
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