The former Liverpool midfielder believes Joachim Low's team lack mental strength and also criticised the coach's decision to rest Mario Gomez for the quarter-final against Greece
Joachim Low's team crashed out at the semi-final stage having been generally regarded as favourites, along with Spain, to win the tournament.
Instead, they suffered a 2-1 defeat at the hands of Italy, and Hamann believes a lack of mental strength has been a problem for the national team in recent tournaments.
"The last four major finals have presented Germany with outstanding opportunities to win some silverware, but when it comes to the crunch we've lacked the mental strength to deal with the pressure," Hamann wrote in his column for the Racing Post.
"We've reached the knock-out stages of the last four major finals, lost in the semis in three of them and the final in the other. And on all four occasions we've looked as though the pressure was too much.
"It's not just our national team. Bayern Munich couldn't cope with the expectation and the pressure when it came to the Champions League final against Chelsea. Brilliant getting to the final, disappointing when it came to the one game that really mattered.
"It's a mindset. Spain are the new Germany. Now you look at the Spanish team and see a team that knows how to play big games. And they look well enough equipped to be able to do so for years to come. It could be a long time before we see Germany back in the winners' enclosure."
Hamann also criticised Low's decision to rest striker Mario Gomez for the quarter-final against Greece after the striker scored three goals in three matches during the group stage.
Germany won the match 4-2 but Hamann thinks that Gomez would have benefitted more from having the chance to continue his good form by starting another match.
"They said resting Mario Gomez was a masterstroke - I think it was the moment Germany threw away their chance of becoming European champions for the first time in 16 years," Hamann claimed.
"Gomez is a striker who needs to play, who needs to score goals. He'd already bagged three goals in three group games and would quite probably have scored against the Greeks. And that would have set the Bayern star up perfectly for the semi-final against Italy.
"Gomez is a streaky player who, if he's on form, doesn't benefit from time off, and I don't think omitting a player in such good form as he was did Germany any favours at all. If Gomez had started against Greece, I'm convinced Germany would be preparing from tomorrow night's final."