Harry's comments were made during a brief visit to Botswana, and he described how the nation was a refuge for him following the death of his mother Diana, Princess of Wales.
The Prince of Wales took his son to Africa after Diana was killed in a Paris car crash in 1997, a decision the duke said allowed him "to get away from it all".
Harry, who was highlighting a forest conservation project in the northern town of Kasane, said there was "undeniable science and facts" behind climate change, and he could not understand how anyone, from children to leaders, denied the science.
He did not mention any individuals by name, but his comments are likely to be interpreted by commentators as a veiled rebuke to climate change sceptic US President Donald Trump.
The president, who has described climate change as a ruse by the Chinese to hurt US manufacturing, has said: "We should be focused on magnificently clean and healthy air and not distracted by the expensive hoax that is global warming!"
Speaking on the banks on the Chobe River, where he helped young children plant Natal mahogany trees, he highlighted the activism of Ms Thunberg, who has sparked the global climate strike movement and addressed a UN one-day summit on the issue this week.
The duke said: "This last week, led by Greta, the world's children are striking.
"There is an emergency, it's a race against time and one in which we are losing, and everyone knows it.
"There is no excuse for not knowing, that I think the most troubling part of it is - I don't believe there is anybody in this world that can deny science, undeniable science and facts.
"Science and facts that have been around the last 30, nearly 40 years, and it's only getting stronger and stronger.
"Genuinely I don't understand how anyone in this world, whoever we are, you, us, children, leaders, whoever it is, no-one can deny science, otherwise we live in a very, very troubling world."
Botswana is a place Harry loves and knows well, and he reportedly whisked his wife there in 2017 to mark her 36th birthday - a year after their love blossomed in the nation during a brief visit soon after they met on a blind date.
Meghan's engagement ring not only features diamonds from the personal collection of Diana, but a stone from Botswana.
The duke, who also helped plant a large baobab tree as part of the project to recreate forest habitat along the banks of the Chobe River, said coming to Botswana gave him: "A sense of escapism...a real sense of purpose."
Harry added: "I came here in 1997, 1998, straight after my mum died, so it was a nice place to get away from it all.
"But now I feel deeply connected to this place and to Africa."