"It is not always the best team in the competition who wins it," said Hodgson.
"But to suggest that because we have qualified from a difficult group makes us one of the favourites, I don't think many people would believe that."
Hodgson's managerial highs
Starts his managerial career with Halmstad in Sweden in 1979, winning two championships
Takes Switzerland to the 1994 World Cup in the United Sates and Euro 96 in England
Guides Inter Milan to the Uefa Cup final in 1997, which ends in defeat by Schalke
Manages Blackburn Rovers into European competition in 1998
Wins the Danish Superliga title with Copenhagen in 2001
Takes Fulham into the Europa League final in 2010
Appointed England manager in 2012
England had only beaten San Marino and Moldova in qualification before this week, but two good performances and wins against
and then Poland ensured the Three Lions qualified for their fifth consecutive World Cup finals.
They finished the campaign unbeaten with 22 points from 10 games, a point ahead of second-placed Ukraine. Their record of just four goals conceded was the equal second best in European qualification, behind Spain.
"We believe we can give a very good account of ourselves and then who knows?" said the 66-year-old.
"The important thing is we are there. We know it is going to be a very tough task, especially in Brazil where a European team has never succeeded before."
He said: "We have grown a lot since the Euros. If I compare today to how we were playing - although the guys did well for me at the Euros - the way the team is playing is pretty different. That is due to two things: evolution, and due to the players now available to us that weren't.
England will not win World Cup - Barnes
"I would like to think the team is progressing, the way we play does improve all the time. If we can keep these players together, who knows?"
The England manager also described reaching next summer's World Cup as his proudest moment in football.
"I think it will top the lot," said Hodgson, who guided Switzerland to the 1994 World Cup in the United States. "I'm English. As an Englishman, it means a little bit more to you.
"I died a thousand deaths every time Poland crossed the halfway line [on Tuesday], which is what you do, but I do think this team is growing now.
"England's a very big football nation. So many people are desperate to see England participate and hopefully do well in a World Cup so we knew it was on our shoulders to make certain we didn't disappoint them."
Former England striker Gary Lineker believes Hodgson is sensible to play down his side's chances of victory in Brazil.
The Match of the Day presenter, who was critical of England's performance after last month's goalless draw in Ukraine,
"Roy Hodgson talking sense in his press conference. Quelling exuberant expectations, without dashing all hope. The voice of reason."
Next summer's tournament will open with Brazil in action in Sao Paulo on 12 June 2014, with the final in Rio de Janeiro on Sunday, 13 July.
The draw takes place in Bahia, Brazil, on 6 December. England have little chance of being seeded given their Fifa ranking of 17 and could be grouped with the hosts.
Englishmen to have led their country to a World Cup
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