The Newcastle United defender spoke to reporters in Kansas City as Thomas Tuchel's squad continued their preparations for Wednesday's Group L opener.
England have not won the World Cup since their triumph on home soil in 1966.
Burn, 34, said there was little point in pretending the squad's ambitions were anything less than lifting the trophy.
"I think it's pointless coming here and saying that we don't want to do that," Burn said.
He referenced the second star that would be added to England's badge if they were to win the tournament.
"That was the challenge, to put a second star on the chest. So that's what we want to do."
England's route into the competition begins with a side that has recent history against them.
Croatia eliminated England at the semi-final stage of the 2018 World Cup in Russia, a result that still carries weight for some of the senior players in Tuchel's squad.
After facing Croatia, England continue their Group L campaign against Ghana and Panama.
Burn, who only made his England debut last year after a career that began in non-league football with Blyth Spartans and Darlington, has spoken about how unlikely his presence in the squad once seemed.
He said the additional wait before England's first match, which arrives almost a week into the tournament, could work in the team's favour rather than against them.
"Now that we're here, I'm really excited," Burn said.
He explained that the early days of the tournament had helped the squad settle into the rhythm of a World Cup before their own involvement begins.
"I think it's when the tournament started that it really began to feel like a World Cup. I don't think it affects us negatively."
Burn said the extra time had allowed the squad to study the tournament from the outside before facing its demands themselves.
"On the contrary, it gives us a bit of extra time to follow the tournament, get used to the intensity of the games, and see what tempo is being played at, before we ourselves have to perform next week."
England have already used their pre-tournament schedule to build momentum, having beaten both New Zealand and Costa Rica in warm-up friendlies in Florida before arriving at their Kansas City base.
Burn's own route to a World Cup finals has taken in spells at Darlington, Fulham, Wigan Athletic and Brighton before a £13m move to Newcastle in January 2022 brought him back to his native North East.
He has since become a first-team regular under Eddie Howe and scored in Newcastle's Carabao Cup final win over Liverpool, a result that played a part in his rise into Tuchel's plans.
For a player who spent years in the lower divisions of English football, simply being part of a World Cup squad carries its own significance, regardless of where the tournament ends.
But Burn's comments leave no doubt that, for the players involved, anything short of a serious push for the trophy would represent a missed opportunity.