Their triumph two years ago, when they beat Germany in the final in Vienna, was their first major trophy in 44 years but goalkeeper Casillas said that was now part of history and the Spanish people wanted more.
"People are not telling us how good we were at Euro 2008," Casillas said in an interview published on the Spanish football federation's website on Monday.
"People are saying we have to win the World Cup. The people want the World Cup," he added.
"We know that the Germany match is the most important in our history, even more than the Euro 2008 final in Austria."
Spain have already made history by progressing to a World Cup knockout semi-final for the first time and play the Germans on Wednesday in Durban for a place in the final at Johannesburg's Soccer City stadium on July 11.
The Spanish finished fourth at the 1950 World Cup in Brazil when the competition had a different format, with a group phase followed by a mini league of four teams deciding who advanced to the final.
"We did not come here to finish fourth," Casillas said.
"The European championships is in the past and was a complete success, it was fantastic," he added.
"Everyone was flying the (Spanish) flag from the rooftops but now, from what we are seeing, this is the most important match for Spain for a very long time."
TEAMWORK COUNTS
Casillas said he had been surprised that some of the world's best forwards, including current World Player of the Year Lionel Messi and his immediate predecessor Cristiano Ronaldo, had exited the tournament in South Africa early.
"This shows that a national team is not at all about only one player," said Casillas, who plays with Ronaldo at La Liga club Real Madrid.
"A player can win you a tournament, like Argentina and (Diego) Maradona (in Mexico in 1986) but today, more and more, the team is what counts.
"A player can perform very well but at the end of the day everything is based around teamwork."
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