Spain won 4-2 on penalties after a goalless draw and Donadoni was quizzed about his future, with 2006 World Cup-winning coach Marcello Lippi tipped to return.
Donadoni said: "It's not up to me. I live day by day and what I experienced at this tournament was positive. Everything we did was for the good of the team.
"We did everything we were capable of, but everyone is free to judge for themselves. I was satisfied with our run.
"I think the players should leave here with their heads held high. They gave everything they had. we've simply got to live with this. Tomorrow is the start of a new era.
"When one loses on penalties, it is obviously very disappointing. We were shattered and tired."
Donadoni added: "I had to study very carefully throughout the match as to who to change and who to bring on."
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