The young Lions had held the early advantage in the shoot-out when Yannick Gerhardt his penalty saved by Jordan Pickford at 1-1 only for Pollersbeck to do likewise in denying Tammy Abraham from the spot.
Germany converted their next three kicks with Redmond's error denying a brave England side who were probably fortunate to see the match go beyond extra-time.
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"We gave our all, we did whatever we could. There were times in the game where, even though I felt they went ahead against the run of play, they came back into it and gave us a lot of problems,” Boothroyd said.
"We had our backs against the wall at times, but we showed real character and determination and we then went ahead and we showed what we are all about.
"Perhaps looking back, we are all deeply disappointed to take it as far as we did.
"I want us to take that next step and we were so close, so close. On tonight, it just wasn't to be."

The Germany team celebrate their side winning a penalty shoot out during the UEFA European Under-21 Championship Semi Final match between England and Germany at Tychy Stadium on June 27, 2017 in Tychy, Poland.

Image credit: Eurosport

Former Northampton Town manager Boothroyd added that he was confident his side could progress.
“I was very confident, I thought looking at the penalty takers, who were going to go out and do it," the 46-year-old added.
"You'd expect them to do what they do all the time, especially when they missed I thought we had a great chance.
"That's football, although not the nicest of feelings, will push them on."
Germany will play Spain in Friday's final after they beat Italy 3-1 in the other semi-final.
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