England will play in Brazil next summer after retaining top spot in their qualifying group with a 2-0 win over Poland at Wembley on Tuesday.
Yet while Hodgson is confident his side will give a good account of themselves at the tournament, he has acknowledged other teams will rightly be considered stronger.
Speaking in his latest press conference, Hodgson said: "We won't be favourites that is for sure.
"I don't imagine any of us will say this is impossible but I will also say and I think the general public will agree, we have been in a slight transition period."
Lineker, who was critical of England's performance after last month's goalless draw in Ukraine, feels that is a good line for the manager to take.
Lineker tweeted: "Roy Hodgson talking sense in his press conference. Quelling exuberant expectations, without dashing all hope. The voice of reason."
Former England winger John Barnes has also sounded a note of caution amid the celebrations following England's qualification.
Barnes does not believe England have enough top-quality players to truly concern the best sides in the world.
It is in his old positions in midfield where the ex-Liverpool star feels the country needs to improve.
Barnes told talkSPORT: "Wayne (Rooney) is our own only truly world-class player.
"Andros Townsend played well but we're not going to win the World Cup by just getting down the wings and putting crosses in.
"We have to develop different types of players rather than just wingers who can get down the line or attacking midfield players."
Another erstwhile England international, Ray Parlour, went further by suggesting the country are lagging a long way behind the world's best.
The former Arsenal midfielder, now a media pundit, said: "Last night was an excellent performance, it was great to get through to Brazil, but I still think England are well short.
"You look at the other nations, the likes of Spain, Holland, France - if they do get through - and then you look at Brazil and Argentina and there is so much quality.
"It is going to be tough for them. I think they are about 25-1 and that reflects roughly their chances. I think that is about the right price.
"They have still got a lot to do to catch up with the bigger nations like Spain."
Prime Minister David Cameron has offered his congratulations to Hodgson and the team following their qualification.
Mr Cameron told MPs during Prime Minister's Questions: "I'm sure the whole House will wish to join me in congratulating the England football team for their excellent win last night, ensuring they qualify for next year's World Cup.
"My commiserations to the other home nations, including Scotland, who had an impressive win over Croatia last night.
"But I'm sure now that everyone in the United Kingdom will swing behind the English team."
Pausing while MPs cheered and laughed, Mr Cameron then added: "You can always dream and hope."