Dyke said he thought Hodgson did "quite a good job" in Brazil and repeated his view that there were too many foreign players in the Premier League for the national team to thrive.
"I've got a lot of time for him (Hodgson)," Dyke told MPs when asked about the England team's performance during a parliamentary hearing.
Dyke said deep-rooted problems in English soccer would make it tough for the national team to repeat their sole World Cup success on home soil in 1966.
"The real problem is there is no pathway for 17 or 18-year-old English boys to get through the system," he said.
"I think it's going to get tougher and tougher unless we do something about it," he said, lamenting the fact that only around 30 percent of Premier League players are English.
He said that world champions Germany had "an unwritten rule" over the number of foreign players in the Bundesliga, creating room for talented German youngsters to come through.
"The other problem we've got is that none of our players play overseas," added Dyke.
Hodgson has also said that English players would benefit from gaining experience by playing abroad and might get more opportunities than they do in the Premier League.
England made an early exit from the World Cup in Brazil last month, picking up only one point from three group games.
However, there has been little clamour for Hodgson to go, with the media and many fans acknowledging the limitations of the current squad.
An FA commission set up by Dyke proposed allowing Premier League clubs to field B teams in lower leagues to help foster young talent but the plan has run into a lot of opposition from smaller clubs and traditionalists.
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- Premier League