But second half goals from Spain's Ruben De la Red and Daniel Guiza saw them finish bottom of Group D with no points.
"I wish we could have at least got a draw," Rehhagel said. "There is no shame in not beating any of these teams.
"Russia beat the Swedes. The Spaniards are outstanding and the Swedes are strong.
"We were the underdog last time and we won. We didn't expect a repeat of that.
"I've said it before, we're a team that finds it hard to score. We never said we'd beat Sweden 3-0, Russia 4-0 and Spain 5-0. We said we'd come here and do what we can."
Goalscorer Charisteas was unhappy with the way the Greeks fell apart in the second half.
He added: "I'm quite upset. We weren't organized properly.
"We believed in victory, that's the way we go into every game. But we didn't get the breaks we needed."
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