Appearing today before the Lord Leveson inquiry, Sally Dowler discussed how the hacking by a private investigator working on behalf of the now-defunct News of the World had given the couple false hope that their daughter was alive.
Mrs Dowler had repeatedly called the 13-year-old's mobile phone in the weeks after she went missing in 2002, but the voicemail had soon become full.
Describing the moment she found that she could get through to the phone again, Mrs Dowler said: "It clicked through onto her voicemail, so I heard her voice and [said], 'She picked up her voicemail, Bob, she's alive'."
She added: "I told my friends, 'She's picked up her voicemail, she's picked up her voicemail'."
Bob and Sally Dowler later learned that the messages had actually been deleted by Glenn Mulcaire, the private investigator who was jailed for phone hacking in 2007.
"As soon as I was told it was about phone hacking, literally I didn't sleep for about three nights because you replay everything in your mind and just think, 'Oh, that makes sense now, that makes sense'," said Mrs Dowler.
The couple also told the inquiry, which is exploring press ethics and standards, how they were secretly photographed by News International's News of the World as they privately reconstructed Milly's last walk in Walton-on-Thames, seven weeks after she disappeared.
Mrs Dowler said: "We put out missing leaflets and a telephone number. That number had changed and I was checking to see if the right poster was up and I was touching the posters to see if they were they were the right ones.
"That Sunday, that photo appeared in the News of the World. I remember seeing it and I was really cross. They had obviously taken the photo with some sort of telephoto lens.
"How on earth did they know we were doing the walk on that day? It felt like such an intrusion into a really, really private grief moment."
The Dowlers told the high court that the "walk was nothing to do with Milly's phone", as the messages were left on "our own home phone or own mobile phones".
Rupert Murdoch, the boss of News International owner News Corporation, was said to be "humbled and very shaken" when he met the Dowlers in July to apologise personally for the hacking of their daughter's phone.
The family also received a £2m settlement from News International over the hacking claims, along with a personal £1m donation from Murdoch to charities of their choice.
Asked what he would say now to the media, Bob Dowler said: "We would sincerely hope that News International and other media organisations would look very carefully how they procure, how they obtain information about stories.
"Obviously, the ramifications are far greater than what appears in the press."
Various high-profile celebrities are also due to appear before the inquiry, starting this afternoon with actor Hugh Grant, who has been a committed campaigner against press intrusion.