Denmark started the tournament with a very fortunate 1-0 win over the Netherlands, who amazingly wasted 28 chances.
But against Portugal the Danes wiped out a 2-0 deficit with 10 minutes left and then suffered the heartbreak of conceding a goal in the 87th minute to lose 3-2 on Wednesday.
"We went for the one point and in a sense we succeeded but the Portuguese were a bit luckier," said coach Morten Olsen.
He soon returned to the topic of fate, declaring: "It's hard to be in these positions and sometimes you're the lucky one and today I think we were a little bit unlucky".
If the team's luck has run out that spells trouble against Germany, who are unlikely to be as profligate as the Dutch attack or as lax as the Portuguese defence, which dozed off twice to let Nicklas Bendtner head two goals.
In truth, Denmark could and should have been 4-1 down by the time Bendtner equalised had Cristiano Ronaldo not wasted two straightforward second-half chances.
Olsen's talk about the vagaries of fate may have been an attempt to obscure an uneven performance by Denmark, who can reach the quarter-finals with a draw against Germany if the Netherlands beat Portugal.
Defender Pepe lost his marker far too easily to head Portugal's opening goal and striker Helder Postiga made Simon Kjaer look like an amateur when he slid in their second.
Apart from Bendtner, who has now scored five goals against Portugal in four competitive matches, Denmark showed little going forward.
Time is surely running out for 33-year-old attacking winger Dennis Rommedahl, who came off injured after his second anonymous performance at the tournament.
Young playmaker Christian Eriksen was largely anonymous again and, to make matters worse, a muscle injury forced off midfield partner Niki Zimling (pictured).
"Our rhythm broke. Zimling is very important for our game and that was a turning point," said Olsen, who was concerned about the possible mental effect of Portugal's late goal.
"These are the kinds of games I hope many players only take part in once, especially the young ones... now we have to pick it up, we have a few injuries, but we'll pick it up before the game against Germany."
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