FA begin year of celebration to mark England's 1966 World Cup Win
He was joined at Tuesday's launch by 1966 World Cup winners Sir Geoff Hurst, Gordon Banks, Martin Peters and George Cohen.
He said "we'll all shoot ourselves" if England fail to progress from their group at Euro 2016.
Roy Hodgson's side have been drawn alongside Wales, Russia and Slovakia for the tournament in France, which starts on 10 June.
"We've got to get out of that group," said Dyke. "If we don't, that really is bad news for English football."
Dyke added he believes England can win the World Cup again "one day soon".
And he said the "building blocks are in place" to emulate that achievement.
"We owe it to a generation of teenage dreamers to show we can do it again," he added.
"The FA is the richest FA in the world, the most income. The FA has to take some of the blame.
"We should have won a tournament in the last 50 years. We haven't. But we will win in the next 50 years, hopefully long before."
England are ninth in the Fifa world rankings and have not gone past the quarter-finals of a World Cup since 1990.
They went out of the 2014 World Cup in Brazil without a win, but Dyke stood by Hodgson.
England won all 10 of their Euro 2016 qualifiers and progress from the group in France "should not be the definition of success", added Dyke.
Dyke said: "It is important to remember and pay tribute to each and every player in the final and also in the squad.
"We hope the celebrations cement the '66 winners their place in history and hope a new generation will hear their story and be inspired by it."
Greg Dyke and Roy Hodgson Greg Dyke backed Roy Hodgson after a disappointing 2014 World Cup
England's recent tournament record
- Euro 2000: Eliminated at group stage
- World Cup 2002: Lost in quarter-finals
- Euro 2004: Lost in quarter-finals
- World Cup 2006: Lost in quarter-finals
- Euro 2008: Failed to qualify
- World Cup 2010: Lost in last 16
- Euro 2012: Lost in quarter-finals
- World Cup 2014: Eliminated at group stage