Germany coach Jurgen Klinsmann hailed the host nation's "fantastic" fans after they beat Argentina on penalties to reach the World Cup semi-finals.
"It's difficult to find words. I'm incredibly happy, proud and thankful," Klinsmann said after the match.
"The fantastic crowd carried us, they believed in us. We knew that even down a goal we'd come back.
"We were convinced that if we got to penalties we'd advance. The belief we have in ourselves is really strong."
Klinsmann said his side - under fire before the tournament began - had acquired a real belief that they could win the tournament on home soil.
We had the luck to do it - it was typically German
Germany's Oliver Neuville
"This is a team that's grown together over the past six weeks and we want to be world champions," he said.
Captain Michael Ballack said the team has deserved their shoot-out win, which came after the match finished 1-1 at the end of extra-time.
"That was sensational. The match was maybe not so interesting for spectators but it was a match at a very high level," he said.
"The team fought to the end."
He added: "Of course, there's always luck when it comes to penalties but I think the team really deserved to win."
Germany will play the winners of the Italy-Ukraine quarter-final in Dortmund on Tuesday at 2000 BST.
"We're on a good run at the moment. Since the start of the World Cup we've done very well and played at a very high level with very few mistakes," said Ballack.
Arsenal goalkeeper Jens Lehmann, who saved from Roberto Ayala and Esteban Cambiasso to set up the shoot-out win, said Germany's past shoot-out success had helped himm.
"As a German goalkeeper it is always expected of you that you will hold up in a penalty shoot-out," he said.
"That was a quarter-final, but the big challenge is coming up now. People should celebrate. I'll get ready for Tuesday."
Substitute Oliver Neuville, who scored the first penalty of the shootout, said: "Either side could have won it. We had the luck to do it. It was typically German.
"Neither team played very well. It was more of a fight. It was a difficult match. Our team didn't have many chances but thank God we won."