"There are certain other fractions that make that tricky for people but the way that I'm constantly inspired every single day is by you guys.
"You don't have to do what you do, you choose to so... I'm going to say thank you."
Harry appeared to be on the video call from the office he shares with his wife at their $21.6 million home in Montecito.
He also told those on the call his family have three "emotional support dogs" – a black Labrador, Pula, as well as rescue beagles Guy and Mia.
The duke, who shares son Archie, three, and 16-month-old daughter Lilibet with his wife, said about the dogs: "Between the three of them they charge around chasing squirrels and causing all sorts of problems for us every day.
"But they're also emotional support dogs – 100 per cent! When they're behaving."
Harry's call was released on Monday and showed his conversations with each of the winners in turn.
When Henry Waine, four, from East Yorkshire, who won the inspirational child aged four to seven category, asked the duke: "How are Archie and Lilibet doing?" Harry responded: "They're doing great – Archie is very, very busy and Lili is learning to use her voice, which is great.
"You sound just like my son Archie. The same little squeaky voice. I love it."