The Three Lions were unbeaten in qualifying, winning their final matches at home against Montenegro and Poland to secure progression to Brazil, but, despite the results being well received, the 66-year-old is cautious to manage expectations.
While he is pleased with the "progress" being made, the England boss points to South American sides' historical success on their own continent as well as his side's "transition period".
"We won't be favourites – that's for sure," Hodgson told the press on Wednesday.
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"We know there are some very, very strong teams in the world, we know that, in South America, the South Americans have yet been unbeaten [in World Cups] and European teams don't win there.
"I don't imagine any of us saying this is impossible but I must also say, and I think the general public will agree with me, that we have been in a slight transition period.
"There are a lot of good young players coming through. We are making progress - I think we are getting better - but whether or not we are at the level of some other teams that one could quite easily name as yet and who are quite clearly bigger favourites than us to win, I don't think any of us would say that."
England wrapped up a berth in Brazil with a 2-0 win over Poland on Tuesday, having thumped Montenegro 4-1 four days previously, and Hodgson revealed how relieved he felt as his team triumphed in both must-win encounters.
"Both games were tense because only one result was possible, there was no safety net – we had to win," he remarked. "If we don't win we don't qualify, basically, so that brings a lot of tension with it, so I suppose I'm happy that those tense days are over."