Dyke, who delivered a state of the game speech on Wednesday, has set England the challenge of aiming for World Cup glory in Qatar in 2022.
The FA chairman also told BBC Radio 4's Today programme: "I don't think anyone realistically thinks we are going to win the World Cup in Brazil."
But Hodgson would not be doing his job properly if he had a similar view, and while England are far from certain to qualify for the tournament, the former Liverpool and Inter Milan boss insists they will be aiming for the trophy should they come through the preliminaries.
Sitting alongside captain Steven Gerrard at a press conference ahead of Friday's qualifier against Moldova, Hodgson said: "What bothers me at the moment is not whether we're going to win the World Cup.
"When we're there we'll try to set about winning it.
"I would say I very much doubt if we're on top of bookmakers' list to win the World Cup anywhere in the world at this moment in time.
"Let's first of all qualify and let's try to get better before Brazil comes around, and let's do our best to win it."
Hodgson's focus has to be on the Moldova game, and Tuesday's match against Ukraine.
He was reluctant to discuss Dyke's speech at all.
"Quite honestly as far as Steven and I are concerned, and that goes for the rest of the players, we've only got one focus," he said.
"I'm not suggesting for one minute we shouldn't think about what's good for English football and how the FA can collaborate better with the Premier League. Of course I endorse all of those things.
"But our concern is can we beat Moldova tomorrow night and then can we get the points we need in Ukraine?
"That's all I'm thinking about and all I'm prepared to talk about."
Dyke believes England should be aiming for the semi-finals of Euro 2020 and then targeting a repeat of their 1966 success when Qatar hosts the World Cup for the first time.
"I don't have any thoughts on that," said 66-year-old Hodgson.
"I presume if you're going to give the speech he gave, it's quite intelligent to have some sort of targets.
"I just feel 2022 might be too far in the distance for me anyway."
Gerrard was not prepared to discuss Dyke's call to arms, stressing all his focus would be on getting to Brazil for what would be his third and final World Cup as an England player.
"I don't want to get involved in a worldwide debate about English football. It's not the right time for that," he said.
"Getting to this World Cup is my priority.
"I won't be around for (future) World Cups.
"None of the players are really talking about Greg's speech."
Dyke also spoke about the dwindling numbers of English footballers playing regular Premier League football, which is as much a concern to Hodgson as it has been to his recent predecessors.
England are struggling in qualification for next year's tournament in Brazil. They are currently second in Group H, two points behind Montenegro, who have played a game more, while Ukraine are just a point behind England.
No European nation has won the World Cup in South America and Dyke therefore thinks England will not be among the favourites for the tournament in Brazil if they qualify.
Dyke added on Today: "I asked a bunch of journalists what would be seen as doing well in Brazil. The consensus was if we reach the quarter-finals we'll do very well.
"That's not to say we can't win. But let's not kid ourselves, it's pretty hard to win in Latin America anyway for a European side. We're certainly not going to go there as odds-on favourites, that's for sure."
Dyke is optimistic England will qualify for next summer's tournament but former striker Gary Lineker labelled Dyke's long-term goals as "fantasy".
Lineker, who scored 48 goals for England, wrote on Twitter: ''Finally read Greg Dyke's speech. Some realism as to issues, some fantasy as to targets. Unless PL & FA unite, it's all pie in the sky.
''Things are improving, small sided games and pitches, better coaching, but will take time and patience. There is NO quick fix!"
Dyke conducted a round of media interviews on Thursday morning following up on his speech, and believes the Premier League understands the need for change without any pressure being exerted upon it. Dyke wants the league's chairman, Anthony Fry, to be part of his commission to look at reforms which could improve the state of the domestic game.
Dyke told talkSPORT: ''I'm not sure I need coercive powers. I think the Premier League understands it is in everybody's interest to have a successful England team.
''I have no doubt some of the remedies might be tough for the Premier League and you might not be able to implement them.''