'That was sensational,' said playmaker Ballack. 'The match was maybe not so interesting for spectators but it was a match at a very high level. The team fought to the end.

The game finished 1-1 after extra time forcing the well-matched teams into a penalty shootout.

'Of course, there's always luck when it comes to penalties but I think the team really deserved to win,' said Ballack.

Coach Juergen Klinsmann added: 'It's difficult to find words. I'm incredibly happy, proud and thankful.

'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. This is a team that's grown together over the past six weeks and we want to be world champions.'

Argentina coach Jose Pekerman, who said he was sure he would not continue in the job, added: 'It was a very exciting match. Argentina also played like favourites and gave of their best although they lost.

'The penalties were a consequence of a very even match. It's a shame for Argentina who played very well today and in the whole championship.'

Germany's Jens Lehmann, who saved two penalties in the shootout from Roberto Ayala and Esteban Cambiasso, was embraced by reserve keeper Oliver Kahn before the spot kicks.

He responded by keeping out Argentina's second and fourth penalties, saying: 'To win the quarter-final is fantastic for us. We had super shots (in the penalties). And it's just expected that a German goalkeeper makes the saves.'

Ballack, referring to Argentina's opening goal scored by Roberto Ayala after 49 minutes, said:

'It was their first chance on that set piece. We knew how they'd do their set pieces. It was a super header from him but our team fought back hard and scored a beautiful goal.

Germany equalised 10 minutes from time with a header by the tournament's top scorer Miroslav Klose before Ballack joined the penalty scorers in the shootout to see Germany through.

'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.

Substitute Oliver Neuville, who also scored in 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.

Neuville, who said he had never thought about losing, added: 'Argentina played a good match but we fought to the last second. Penalties at the end are about luck but we were able to keep our nerve. I wanted to take (one) and thank God it worked out.'

Germany will play Italy or Ukraine in the semifinals.