The prince was speaking after a tour that saw questions raised about the role of the royals in the Caribbean.
The future relationship between the UK and Belize, Jamaica and the Bahamas is for their people to decide, the Duke of Cambridge has said.
He said that he and the duchess were "committed to service" and that "for us that's not telling people what to do".
's comments come after an eight-day tour of the Caribbean nations to mark the Queen's Platinum Jubilee.
The trip saw the Jamaican prime minister publicly tell the royal couple that his country would be "moving on".
It also came four months after Barbados replaced the Queen with an elected president.
In a written statement reflecting on the trip, the prince said foreign tours were an "opportunity to reflect".
"You learn so much," he said. "What is on the minds of prime ministers. The hopes and ambitions of school children. The day-to-day challenges faced by families and communities."
The trip saw the duke and duchess visit Belize and Jamaica before a final stop in the Bahamas.
The Bahamas leg included a trip to a primary school, where the duchess spoke to pupils about the importance of being able to reconnect after being separated during the pandemic.
The couple also visited a church on the Abaco Islands to speak to locals about destruction caused by Hurricane Dorian in 2019, and a coral conservation project that was among last year's winners of the Royal Foundation's Earthshot Prize for contributions to environmentalism.
The duke continued: "I know that this tour has brought into even sharper focus questions about the past and the future.
"In Belize, Jamaica and the Bahamas, that future is for the people to decide upon."
After the couple left Belize on Tuesday, a government minister announced a new commission would begin consulting with people across the country on how the "decolonization process" should proceed.
Bahamian Prime Minister Philip Davis has not commented on the issue, although last year said it was "not on the agenda".
However, the day before the duke and duchess arrived in the Bahamas, a letter was released by campaign group The National Reparations Committee, calling for Britain to pay reparations for the slave trade.
In the statement, the duke said he and his wife saw the purpose of their roles as being to serve and support people "in whatever way they think best, by using the platform we are lucky to have".
"Who the Commonwealth chooses to lead its family in the future isn't what is on my mind," he said. "What matters to us is the potential the Commonwealth family has to create a better future for the people who form it."