The Under-19s, drawn to go to Denmark for the second round play-off tie after coming second in their group earlier in the season, took an early lead through Salvatore Pezzella's deflected effort - only for a penalty soon after to erase the advantage.
A scrappy game did not see another goal before the 90 minutes was up, sending the match to penalties.
The Danish champions clinched a 4-2 victory from the spot, ensuring it will be they who progress to the last-16 of the tournament.
"All the guys played well," De Rossi said afterwards.
"Apart from at the start of the second half, when he struggled a bit, we did well and played the way we wanted to. Clearly, though, we were lacking that little something to decide the game.
"It's a shame to go out on penalties, but anything can happen at that point."
See photos from the game at the MCH Arena in the gallery below.
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