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Spain must beat Chile and Honduras in the remaining gropu games to be assured of progressing, but Del Bosque will not change his attacking style in favour of a more conservative approach.
"Each game is different," he said. "We have arrived up to here playing a certain way and we will not lose our identity. In football you can always lose but I feel a sense of avenging this defeat."
Hitzfeld, meanwhile, was all smiles after his team claimed their first win over Spain.
"I am fully aware that we have made history," he said. "This will go down in the record books. The three points is a gift that we happily accept. It's a great feeling to start the tournament with three points against one of the biggest contenders for the title.
Hitzfeld showered his team with praise. "I am very satisfied with my team's performance," he said. "Our aim today was to have two compact lines behind our strikers as we didn't want to lose too much energy fighting for the ball. We wanted to focus on our defence and wait for the counter attack.
"We concentrated and were organised from the start. We didn't allow any chances for Spain in the first half and that gave us self-confidence.
"In the second half, Spain rolled one attack after another and we knew they would open their defence. After we took the lead, we gained even more confidence."
Hitzfeld made no apologies for his tactics. "If you want to play an attacking game against Spain you would lose by a big margin," he said.
The only negative aspect of the match for the Swiss was the injury to Philippe Senderos. The Fulham defender was substituted midway through the first half after sustaining an ankle problem.
"Senderos has a sprained ankle and he may have a ruptured a ligament or worse," said Hitzfeld. "He has to go to hospital to have some tests. It will be very difficult to replace him and it will be a major blow for my team if we were to lose him."