The 18-year-old made the move to Goodison Park with hours left of the January transfer window despite interest from a host of other Premier League sides.
The Tykes boss says he feels "numb" after losing the highly-rated right-back to David Moyes' side, but believes he will become one of the top defenders in the Premier League for the Toffees.
"On Wednesday, I was pretty confident that we would keep John [Stones]," he told reporters. "But then I got a call on Thursday morning to say that he would probably be leaving.
"To be honest, I am numb. It is like losing a member of your own family."
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The England Under-19 international signed a deal on Merseyside for five-and-a-half years, and Flitcroft believes the defender is simply irreplaceable.
"I was asked if I could replace him, and the answer was 'No.' How do you replace the best young defender in England?
"There is nobody out there as good as John, and that is why clubs were prepared to pay £3million for him."