The former England football star said his account was hit 23 times in two days.
Gascoigne said he knew who had taken the money but did not know exactly how much had gone, valuing the loss at between £9,000 and £50,000.
Speaking outside his home in Bournemouth, Gascoigne told The Sun: "I know who did it. I know how it f****** happened, there were 23 hits in f****** two days. It was quite a lot of money.
"It wasn't that much. F*** knows. I don't know. Website, internet, I've not got a clue."
The 46-year-old was once worth a reported £14 million, but avoided bankruptcy in 2011 after agreeing an out-of-court deal over an unpaid £32,000 tax bill.
Gascoigne, who has publicly battled alcoholism, recently relapsed after several sober months following a spell in rehab earlier this year.
He was apparently pictured drinking gin in an off-licence in July, and this month was seen stumbling around an betting shop.
Ealier this week he told an ITV documentary: “I hope I don’t die through it (drink), because I won’t get any sympathy because, well, he was warned.
“I know probably in the future I am going to drink again. I just don’t know why I f***ing pick up the drink.”
Gascoigne, widely acknowledged as the most talented English player of his generation, won 57 England caps between 1988 and 1998.
His clubs included Newcastle United, Tottenham Hotspur, Lazio, Rangers, Middlesbrough and Everton.