The prince was speaking at the Travalyst event being held in the Scottish capital.
Ahead of the short speech, event host Ayesha Hazarika told the gathering: "He's made it clear that we are all just to call him Harry."
Within weeks, the Queen's grandson and his wife, Meghan, will officially step away from royal duties.
In his address, Prince Harry - who is known as the Earl of Dumbarton when he is in Scotland - warned that the growth of tourism was threatening to destroy some of the world's most beautiful places.
