"What bothers me is not whether we win the World Cup; it's giving the performances we need to make sure we make the World Cup," added the England manager.
Key points of Dyke's speech
Sets target to reach the semi-finals at Euro 2020 and win the World Cup in 2022.
Describes English game as a "tanker which needs turning" citing the amount of foreign players limiting chances for English players.
Wants more English players who are consistent starters in the Premier League
Aims to set up an FA Commission asking why so few players registered for England play in the Premier League with help from Premier League, Football League, the LMA and PFA
Dyke also said he was open to: exploration of a quota system for foreign players; examining the current work permit system; examining the loan system and evaluating the pros and cons of a mid-season break.
England captain Steven Gerrard also revealed focus within the squad is on their upcoming World Cup qualifiers.
"I don't want to get involved in a worldwide debate about English football. Getting to this World Cup is my priority," said the Liverpool midfielder.
"There hasn't been a reaction. None of the players are talking about what Greg said. They're all focused on getting the six points from these two games.
"We're focused on a strong performance. It won't be on proving any individuals wrong."
In Wednesday's wide-ranging speech, Dyke warned England may not be able to compete seriously on the world stage without changes in the domestic game.
The FA chairman will set up a commission to ask key questions on how England can change its long-term prospects.
He described the English game as a "tanker which needs turning" citing the amount of foreign players limiting chances for English players.
Phil McNultyChief football writer
"Greg Dyke speaks a language the football fan understands. Whether it is something the Premier League and others are willing to understand as his tenure begins is another matter."
Dyke also said he was open to an exploration of a quota system for foreign players, examining the current work permit system, examining the loan system and evaluating the pros and cons of a mid-season break.
"I endorse the things the chairman said," said Hodgson.
"I saw the speech beforehand. I haven't followed all of the responses to it.
"We've only got one focus. I'm not suggesting we shouldn't think about what's good for English football but our concern is can we beat Moldova and get the points we need in Ukraine?"
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