Sven Goran Eriksson's men bowed out in the quarter-finals to the tournament favourites on Friday after Rivaldo and Ronaldhino cancelled out Michael Owen's opener.
Summer recruit Jamie insists England's youngsters will only reap the benefit of their experiences in the Far East and should be challenging at the next major tournament, Euro 2004, with the talent coming through the ranks - including his new team-mate Ledley King.
Jamie, just back from training camp in La Manga, said: "It was a little disappointing in the end. We all felt we could win it, perhaps we were all carried away with it all and it's a shame it didn't work out for us.
"Maybe the next European Championship in 2004 or even the next World Cup will be the tournaments we can flourish in.
"If we can keep the quality young players coming through - and I expect Ledley King to have a big part to play - then that will be a more realistic target for us than this World Cup."
Jamie says the continuining surprise element in the tournament suggests that the gap between football continents is closing.
"It's been exciting," added Jamie, who saw plenty of the early matches as a pundit for the BBC. "And it shows that the gulf between the likes of Africa and Asia and the rest of the world is getting smaller.
"Japan and South Korea have been a revelation out there. The players are so fit and play at such a high tempo. It will be interesting to see if any of those players come to the Premiership and if they could make a go of it in England."
Jamie Redknapp says England can look forward to a bright future after their World Cup exit against Brazil.