Only a dramatic 9-8 defeat by France prevented Warren Gatland's side from reaching the final in a campaign that surpassed all expectations.
The team's youthful exuberance was a key factor behind their success, but the pressure on their shoulders has now risen significantly.
Warburton hopes his players are able to emulate level-headed outlook that enabled them to flourish in New Zealand.
"It was a missed opportunity in New Zealand because we missed out on getting to the final by one point," said Warburton.
"Maybe we were a little bit naive out there in that we didn't realise how big a stage we were playing on.
"We played each game as just another rugby match. We played with no fear and never went into our shells.
"That will probably be the same message this time - don't think too much about it and ignore all the stuff that goes on off the field. It's just another game of rugby.
"It will be different in the Six Nations because the pressure from the Welsh public wasn't there going into the World Cup.
"We surprised people with how far we got in the competition, but now we're expected to win the Six Nations.
"I was walking past the Millennium Stadium the other day and it said we have three home games, the last of which is Wales v France... and that was the one that had sold out.
"Obviously everyone is anticipating that as the championship-winning game. There is more pressure on us, but we're happy with that."
Coach Warren Gatland believes Welsh rugby has a bright future thanks to the ability and attitude of its emerging stars.
"We've got some real quality and talent. Some of our young players are very exciting and incredibly professional in the way they prepare," Gatland said.
"I believe we have a special group of young players who will only improve from here.
"What this team is potentially capable of doing is very exciting for Welsh rugby."
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