Hitzfeld, the former Champions League winning coach of Bayern Munich and Borussia Dortmund, instructed his players to shut Spain out of the centre of the field and force the talented European champions on to the flanks.
"The players showed resolve, they also behaved cleverly from a tactical standpoint. They quite deliberately left some space for the Spanish team and very much followed instructions," Hitzfeld told a news conference.
"We said we wanted to close down the centre completely and force the Spaniards to come by the sides because we knew when they have to play high crosses into the penalty area we would be the stronger team," the German said.
Switzerland's defence and midfield dwarfed many of the Spanish side. The underdogs started with four players at least 1.90 metres tall and only had one player shorter than 1.80 metres, unlike Spain's five.
It was the first time Switzerland had beaten Spain in 19 attempts, a victory Hitzfeld had predicted at a news conference a day earlier.
Spain monopolised the ball at the start of the game and they clearly hoped the Swiss players would run out of steam but Hitzfeld had told them to conserve their strength.
"We also said we didn't want to lose too much energy fighting for the ball in the opponents' half. We said we wanted to focus on our defence and to wait for counter-attacks."
"If you want to play an attacking game against Spain you will lose out massively because they will score one goal after the next," he said.
He praised impressive goalkeeper Diego Benaglio as one of the match winners, along with goal scorer Gelson Fernandes who was one of the few Swiss players to needle the Spanish midfield.
"He's great in motivating the team even if he's just on the bench. For me, as a coach, he's an extremely precious and extremely valuable player. You just love such players," he said.
While the coach said the ankle injury to defender Philippe Senderos could be serious and force him out of the competition, one of the team's doctors was more optimistic.
"For now we think there is no bone fracture and all being equal he should be available for the next game," said medic Cuno Wetzel.
The thrilled Swiss players were also full of plaudits for Hitzfeld, a coach who has won seven Bundesliga titles.
"I can say we owe this victory to the coach. He had a lot of confidence, told us what to do, we followed his instructions and won," said striker Eren Derdiyok, whose powerful run into the box made the goal for Fernandes.
"Winning against Spain is like a dream."
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