Fabregas has had to play a substitutes' role all tournament - and in the final - but he said the victory made up for all the frustration.
He said: "This is an historic moment for Spain and it may never be repeated - and I dedicate this to my whole family.
"I was a bit down because I had not played as much as I had wanted but in the end it has all been worth it.
"The fans have fantastic, the rock on which we base everything and I hope in two years' time we will have more joy at the Euros."
The match saw 14 yellow cards - two leading to one red card for Everton's John Heitinga - handed out by English referee Howard Webb. That is easily a record for a final and Iniesta admitted it the Dutch adopted a rugged approach.
Iniesta said: "I had the opportunity to score that goal which was so important for my team, and it's incredible.
"I've made a small contribution in a very tough game, a very rough game - there were all sorts of things happening on the pitch.
"Spain deserved to win this World Cup. It's something we have to remember and enjoy, and should feel very proud of everyone in this squad.
"The manner in which it happened, we gave everything," Iniesta said. "To win the World Cup there are no words to describe it.
After he scored Iniesta took off his shirt to reveal a T-shirt paying tribute to Dani Jarque, the Espanyol player who died after a heart attack in August.
The T-shirt said "Dani Jarque is always with us" and Iniesta explained: "I wanted to carry Dani Jarque with me and with my other team-mates.
"We wanted to feel his strength. We wanted to pay tribute to him in the world of football, and this was the best opportunity to do so."
Spain's triumph had been predicted by Paul, the psychic German octopus and Iniesta added: "As for the octopus, what can I say? We won. The octopus will be very popular in Spain."
Spain coach Vicente del Bosque refused to criticise Holland for their approach.
He said: "First of all I should congratulate our opponents. They made it very difficult for us to play comfortably.
"It's been a very intense match, and congratulations to them.
"Fabregas came on and we began to dominate. We had greater ball possession and depth in our game.
"We created chances for Cesc and David Villa which we could have converted, but that's the way football goes."
Del Bosque said the whole of the country deserved to share in the jubilation.
He added: "The dressing room is delighted, ecstatic. But Spain, the country, deserves this triumph, this World Cup.
"This goes beyond sport. We have to celebrate. All the people have been behind us in Spain, and we're delighted to reward them with this victory."
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