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"Full credit goes to Germany," said U.S. coach John Hackworth. "They are an outstanding team and we wish them all the best going forward. We didn't play as well as we thought we could."
The Germans, who meet England in the quarterfinals, had tied Colombia (3-3), beat Ghana (2-1) and Trinidad & Tobago (5-0) in group play.
The Americans suffered losses to Tajikistan (4-3) and Tunisia (3-1) before the win over Belgium earned them second place in Group E.
The U.S. loss to Germany marks the third straight time the USA lost its first second-round game at the U-17 World Cup. Only in 1999, when they finished fourth, has the USA won a second-round game in its record 12 finals' appearances.
The Germans committed 27 fouls compared to the USA's 10, but the Americans' free kicks caused little trouble.
Long throw-ins by Sheanon Williams were a key U.S. weapon and out one of them came a goalmouth scramble from which Bates managed to shoot into the net while on the ground with his back to the goal.
"Everybody at this point in the tournament has put in so much hard work and made so many sacrifices in their lives," said Hackworth. "You want to go farther and we feel like we should be going on but eventually it's going to come to an end, and this is very hard to swallow. You're with these guys for two years, so it's hard to take right now."
Asked what his team has learned its World Cup experience, Hackworth said:
"They'll probably have learned that they came here and we didn't play the way we're capable of and that put us in a big hole. We did show a lot of character and came back and played some very good soccer, despite having our backs against the wall and having to take on one of the best teams in the world in Germany, and fight them until the final whistle.
"Hopefully that will live on in these players minds for a long time, and they'll have some of that hurt of not going on to drive them as they develop."
Aug. 30 in Cheonan, South Korea
Germany 2 USA 1
Goals: Sukuta-Pasu (Kroos) 65, Sukuta-Pasu (Kroos) 89; Bates 92+.
Germany - Vollath, Strifler, Teixeira, Rausch, Wolze, Sukuta-Pasu (Esswein, 94), Kroos, Dowidat, Rudy, Erb, Bigalke (Sauerbier, 91).
Coach: Heiko Herrlich
USA - Lambo, Williams, Bates, Meyer, Zimmerman, Wenzel (Cruz, 83), Jeffrey, Garza (Ibrahim, 46), Nimo, Urso (Dominguez, 75), McLoughlin.
Coach: John Hackworth
Shots on goal: 10-5
Corner Kicks: 8-4
Yellow cards: USA - Williams 20, Zimmerman 68, Wenzel 74.
Referee: Craig Thomson (SCO)