The holders clinched a place in Sunday's title decider against Germany or Italy in part thanks to a Casillas save in the 4-2 penalty shootout win over Portugal on Wednesday and he said Spaniards should enjoy the moment while it lasts.
"It's strange what happens in life sometimes," the 31-year-old known as "Saint Iker" told Spanish radio station Cadena Ser.
"However badly things are going for the country in terms of the crisis and all that, football has been a kind of oasis that has allowed people to forget everything a little bit," he added.
Spain has suffered from soaring borrowing costs amidst a debt crisis and economic downturn that has hit much of Europe.
"Football has been a source of joy and we are happy and excited about that and we want people to make the most of it as it will be difficult to repeat," added Casillas.
By seeing off the Portuguese, Spain join the West Germany team of the 1970s as the only sides to reach three successive finals at European championships and world cups.
They can eclipse the Germans - who won the 1972 European Championship and 1974 World Cup but lost the 1976 Euro final to Czechoslovakia - with victory in Kiev.
They would then become the first nation to win back-to-back continental titles with a World Cup in between.
Casillas missed out on a personal milestone on Wednesday as he remains one short of becoming the first player to notch up 100 victories in internationals.
His 136th appearance will go on record as a draw after the Iberian neighbours were locked at 0-0 after 120 minutes and needed spot kicks to separate them.
Casillas said he remembered the excitement he felt when Spain won soccer gold at the Barcelona Olympic Games in 1992 when he was 11 years old.
"These have been four exceptional years and the kids back home don't realise how lucky they are to be able to experience this," he said.
"I remember winning the gold in '92 and that was incredible so imagine what they are feeling now."
A Spanish triumph on Sunday would make Vicente del Bosque the first coach to win a treble of World Cup, European Championship and Champions League, Europe's elite club competition.
He led Spain to their first World Cup triumph in South Africa two years ago and took Real Madrid to the Champions League title in 2000 and 2002.
In typically modest fashion, Del Bosque said it was all down to the players.
"I think this is an extraordinary group and despite the long season we have behind us they are playing with great generosity and great effort," he told Cadena Ser. "Such good players make any coach look good."
Germany play Italy in Thursday's second semi-final in Warsaw.
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