Costa Rica beat Italy on Friday to seal their progression from Group D and consign the Three Lions to a first group-stage exit since the 1958 edition of the tournament.
"Gerrard and the English defence must take the blame for both Uruguay goals. When [Nicolas] Lodeiro started his run before the first, Gerrard could have done better," the Argentina legend wrote in his column for The Times of India.
"It was Gerrard again who made a mess of a long shot from the Uruguayan goalkeeper after England had equalised. The ball went to Suarez, who once again found a lot of room in the penalty area before unleashing a ferocious shot.
"You can't afford [to do] that with a striker of his class and England paid the price."
Roy Hodgson's side conclude their campaign by facing the Costa Ricans on Tuesday, while Italy and Uruguay battle it out to join the Caribbean team in the last-16 stage.