Australia didn't loss a match in the tri-series, which culminated with a win against England in the Final last Sunday.
Warne said they had taken advice from 1992 World Cup veterans Geoff Marsh and Craig McDermott about the expectations of playing on home soil.
"They sort of said they thought it was going to happen (winning the World Cup) when they were here on home soil," Warner was quoted as saying in cricket Australia website.
"We can't be too complacent, we've got to keep backing ourselves, and this tri-series was a great message to the rest of the world coming out here that we mean business.
Warner also said there were no pressure on them.
"People think there's a lot of expectation and pressure on us but we don't see that at all. We see it as another game and we've got to win every game to win that World Cup," the left-hander said.
"I know me and Finchy (fellow opener Aaron Finch) have spoken about it as opening batsmen that we can really dominate and see a clear message that we mean business."