Castro, who resigned the Cuban presidency last year due to ill health, also said the men were removed as "the external enemy filled itself with expectations for them," although it was not clear who this referred to.
Both Roque and Lage had been mooted as possible future leaders of Cuba after the Castro brothers leave the Cuban political scene.
It is not clear what the moves will mean for future US-Cuba relations, although Barack Obama, the US president, has said he was willing to talk with Cuban leaders and wants to loosen restrictions on travel to the island by Cuban-Americans.
At least 20 officials were shifted, demoted or promoted in Cuba's government on Monday, in a move the government said was intended to make Cuba's government more compact and functional and to work towards "perfecting" the Cuban system.
Roque who had been Havana's chief diplomat since May 1999, was replaced by his deputy, Bruno Rodriguez.
And Lage, a vice-president who had far-reaching economic powers, was also removed from his post as executive secretary of the Council of Ministers, but it was not clear whether he would stay on as one of the vice-presidents of the Council of State.
He was replaced as cabinet secretary by General Jose Amado Ricardo Guerra, a former top military official.
Lage had been credited with helping to save Cuba's economy by implementing economic reforms after aid from the Soviet Union ended in the early 1990s, while Perez Roque was once personal secretary to Fidel and a former leader of the Communist Party's youth organisation.
In addition Jose Luis Rodriguez, the economy minister, Raul de la Nuez, the minister of foreign trade, and Jose Luis Gacia, the minister of economy and planning, were also removed from their posts.
Georgina Barreiro Fajardo, the finance minister, and Alfredo Morales Cartaya, the labour minister, were also fired and the ministries of fishing and food combined as part of the changes, as were the ministries of foreign investment and foreign trade.