Daltrey, frontman of The Who, yesterday revealed it was Donegan's freedom of expression and fluid style that helped him find his own voice.
"I love performing - I love getting out of myself and singing," he said. "I love that world that you have to enter to sing a song well. My style, the way I sing, and the freedom that I always try and sing with, was inspired by Lonnie Donegan - the Glaswegian.
"When I saw him sing I just thought 'Wow, he's just letting himself go, being totally true to how he was feeling at that moment'. He never ever cheated it, and I just try and do the same."
Donegan was one of the first British pop stars to make it big in America and the man whose rough and ready take on US folk spurred other artists including Joe Cocker and John Lennon.
He was born in Glasgow to an Irish mother and Scots father. He grew up in the east end of London but saw himself as a Scot.
His son Peter Donegan, who now sings with the Lonnie Donegan band, said his father's inimitable style had shaped the careers of many singing stars.
He said: "He was the start of a massive leap in the British music industry away from mainstream people like Max Bygraves. It made people realise they didn't have to be amazingly musically adept to write or produce a song. All they needed was a good three chords and then to take off and go with it."
Lennon said that Donegan inspired him to start the Quarrymen before The Beatles were formed, while Cocker described hearing Donegan's cover of Rock Island Line on the radio as life-changing.
Peter Donegan said his father was born in Bridgeton and he was extremely proud of being a Scot. "It always felt like a homecoming for him whenever he used to come back to Scotland and perform," he said.
Donegan fell in love with American music when he was stationed in Vienna doing national service and used to listen to artists such as Leadbelly on American forces radio.
Daltrey, 67, said becoming famous in the early 1960s was like "walking down Sauchiehall Street with a crowd and they're all walking with you, and the second you become famous they all turn round and start walking towards you. It happens very quickly as soon as you get a hit record. It's very strange to deal with as an artist."
He also said he had never been tempted to get involved in drugs. "I used to be the one who had to rein it in and get these people back home safely.
"I had to get them all the way up to San Francisco and back to England, all on acid.You try that, with Keith Moon, John Entwistle and Pete Townshend when they were 22 years old. That was my job, and I got them home safely."
Daltrey was interviewed for BBC Radio Scotland's Musical Legends, to be broadcast on Wednesday.