Both countries have been drawn to play in Group D at Brazil 2014, alongside Italy and Uruguay.
As they are ranked 31st in the FIFA World Rankings, 18 places below England, Costa Rica are expected to be the group's stereotypical whipping boys.
However, Milutinovic believes that the Three Lions could struggle to live up to their tag of clear favourites when the sides clash in Belo Horizonte on June 24.
"At this World Cup there will be some great coaches," Milutinovic told reporters. "Roy Hodgson is a great coach and England have some good players.
"The question, for me, is whether they can show it on the field. I don't know if they can.
"But I think Costa Rica have the mentality to beat England. In fact, I know they do because of what happened with my side in 1990."
Milutinovic masterminded Costa Rica's 1-0 win over Scotland at Italia '90, where his side reached the knockout stages after also beating Sweden in the group phase.