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He made the frank admission on BBC Radio 4's Desert Island Discs feature, where guests are interviewed by host Lauren Laverne.
Radcliffe, 30, said: "If I went out and if I got drunk, I'd suddenly be aware of there being interest in that because it's not just a drunk guy. It's 'Oh, Harry Potter's getting drunk in the bar.'"
Speaking about the start of his career where he was a child star, the actor opened up about the perception of him. He said playing the wizard 'carried some kind of interest for people and also a slightly mocking interest'.
He added: "It's inherently funny for people."
Speaking to Laverne, he continued on to say that his way of dealing with his fame was to drink more often, saying: "I did a lot of that for a few years."
Radcliffe, who first appeared as the character when he was just 11 years old, said: "A lot of drinking that happened towards the end of Potter and for a little bit after it finished, it was panic, a little bit not knowing what to do next - not being comfortable enough in who I was to remain sober."
It's not the first time the star, who has been sober since 2010, has spoken about his struggle with fame and attention, as well as deciding what to do when he no longer played the role that made him famous.
Speaking to Off Camera last year, he said: "In my case, the quickest way to forget about the fact that you're being watched is to get very drunk.
"And then as you get very drunk, you become aware that 'Oh, people are watching more now because now I'm getting very drunk, so I should probably drink more to ignore that more.'"
He also spoke to Laverne about dealing with being a child star, and what happens when they outgrow a role.
He said: "They are by that point the breadwinner for their family. So multiple people are now reliant on them continuing to do this job and they feel pressured into it and forced into it.
"I think that's why you can see people go to drink and drugs because it is fun and they're available and it seems like a good idea.
"There's nobody around you talking about the consequences or being honest with you about that."
Desert Island Discs is available to listen to on BBC Sounds.
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