Kroos came out of international retirement for one last dance with Germany at the Euros, playing a crucial role as the home side impressed after almost a decade of poor performances at major tournaments.
He had previously announced he would retire from all football after the tournament.
After a goalless first half, Spain took the lead when Dani Olmo swept in a pass from 16-year-old winger Lamine Yamal.
Germany hit back in the 89th minute when Florian Wirtz equalised, sending the game to extra time.
Germany had a penalty appeal for handball turned down before Spain's Mikel Merino headed in the winner in the 119th minute.
"We threw everything in, to lose when we were so close, is bitter," Kroos told ARD.
"The elimination is the main focus right now (rather than his retirement), because the goal that we had we were unable to achieve and the dream we had is over.
"We played a good tournament but when you're so close, to be eliminated like that, it's bitter."
The 34-year-old insisted the future was bright for German football and said the side had brought optimism back to the fans and supporters.
"We can all be proud because of what we did. I was happy to help out, I think we gave German football hope again and we got better as we went along.
"I think the team will do it in future, but today we're extremely sad because we would have liked to stay a little longer."
