The Three Lions will begin the finals against the Italians in Manaus. They then face Uruguay in São Paulo, and, finally, Costa Rica in Belo Horizonte.
Dyke reacted after England were the final team placed in Group D.
"It's a tough group, there's no doubt about that," Roy Hodgson told the BBC. "We've got almost two number one seeds in our group. The good thing about Italy, I suppose, is we do know each other and the other thing is that , with the climate in Manaus, it's against another European team, so we'll both be in the same boat."
"It's quite difficult to put a positive spin on the quality of our opponents. It will be a chance to see the north of Brazil. I've never been to the Amazon."
World Cup winners Spain will take on 2010 finalists Netherlands in the group stage on the second day, while Germany versus Portugal on 16 June is another stand-out fixture from the group stage.
Brazil will kick-off the finals against Croatia on 12 June.
England were knocked out of the 2012 European Championship by Italy on penalties and last played them at a World Cup in the third/fourth place playoff at Italia '90.
Alf Ramsey's Lions began their victorious 1966 campaign with a goalless draw against Uruguay at Wembley, but have never played Costa Rica before.
England's last fixture with Uruguay came in 2006, when Peter Crouch nodded in a late winner at Anfield.
Hodgson earlier this week admitted he wanted to avoid playing in Manaus earlier this week, due to the difficult climate.
Highs rise to a sweltering 30C with a 40% chance of thunderstorms in June, and humidity up to 80%.
England v Italy - Manaus Sunday 15 June (02:00 BST)
Uruguay v England - Sao Paulo Thursday 19 June (20:00 BST)
Costa Rica v England - Belo Horizonte Tuesday 24 June (17:00 BST)
FULL WORLD CUP DRAW