Spain captain Iker Casillas concedes it will take time for him and his team-mates to realise the magnitude of their World Cup victory.
Vicente del Bosque's team, who have been one of the biggest underachievers in the game's history, capped a remarkable two years by adding the world title to their Euro 2008 triumph.
Andres Iniesta grabbed the only goal deep into in extra-time to break Holland hearts and earn his team a place in history.
"It's a historic moment for Spanish football," the Real Madrid goalkeeper said. "This achievement is something that we, the players, are still not aware of...what the significance really is.
"I think it's something we will only realise over time."
Casillas also walked away with the Golden Glove awarded, handed to the best goalkeeper in the competition, for his overall efforts in South Africa.
The 29-year-old, a veteran of more than 100 caps, was mainly a spectator against the Dutch, but had to make two crucial saves from Arjen Robben either side of half-time.
He refused to take any individual plaudits, saying: "I'm not a saint, not at all. I have a lot of experience after putting in a lot.
"I have been gifted and have had lots of support from all my family and friends, so I am really overjoyed today."
And he hailed the team's overall display at the finals, rating it even higher than the European success two years ago.
He added: "It's what we have dreamt of since we were children. It is truly a special time and certainly a much happier moment than when we won the European championships. We are now the world champions.
"It was not easy, but luckily we managed to win. We've earned this victory from beginning to end.
"It's been almost 50 days of full concentration. That in itself is very complicated, very difficult and gives an idea of what this group has done."
Holland midfielder Nigel de Jong felt his side were let down by their lack of cutting edge.
Despite being overrun for most parts of the game, Robben missed a fine one-on-one chance, which eventually proved a turning point.
The Manchester City player said: "It was a close game from both sides.
"We both created some very good chances and both knew that if they'd score first then they would win the game.
"So I think it was really balanced. Spain really have a good team, but so do we. As I said we created a lot of chances and you have to take your chances, that's all."
