Christian Solidarity Worldwide (CSW) has been speaking as the former revolutionary, who was seen as both pariah and people's champion, died on Friday night aged 90.
The socialist revolutionary's death was announced by his brother, Raul Castro, the incumbent Cuban president, on state television.
He ended the announcement by shouting the revolutionary slogan: "Toward victory, always!"
Mervyn Thomas from CSW told Premier that life has not been good to Christians under the Communist government in Cuba.
He said: "Many of the country will be in mourning today, and we join them in mourning for a man that has had a significant impact in the world.
"But my prayer is that the country will take stock and deliver really religious freedom and religious rights to every person in the population, every citizen of Cuba at this time."
Fidel Castro led a guerrilla coup in 1959 to overthrow the regime of the US-backed former Cuban president Fulgencio Batista, and remained hostile to Washington throughout his life.
Mr Castro's last appearance in public was at an event to mark his birthday.
The gala celebrated key moments in his life, including repelling the US-backed attempt to invade in the Bay of Pigs in 1961.
Mervyn Thomas said that under current president Raul Castro life for Christians had been even more restrictive in the Communist state.
He said there were: "Restrictions on religious freedom, restrictions on registration for churches and anyone who spoke up for human rights were not treated well."
He went on: "Things have not improved, in fact in some respects over the last couple of years it seems to have got worse.
"But whether this will be an opportunity for people in the country to have more of a say, I really don't know, we'll just have to wait and see."
Pope Francis sent a telegram to Raul Castro offering "my sense of grief to your excellency and family".
In a sign of his personal esteem, Francis signed the telegram, breaking from the Vatican's usual practice of have the secretary of state send such messages.
Pope Francis met Castro during the papal visit to Cuba in September 2015.
Castro was born on August 13th 1926 in eastern Cuba.
Listen to Premier's Hannah Tooley speak to Mervyn Thomas here:
