Despite winning twice on the PGA Tour last year, Bradley missed out on one of the six automatic qualifying places on the US team.
He finished 11th overall but was then overlooked when captain Johnson selected six wildcard picks for Rome, with Justin Thomas and Rickie Fowler selected despite being lower down the rankings.
Bradley was being filmed at home for the Netflix documentary Full Swing when Johnson phoned to tell him he would not make the team.
His disappointment was obvious, as he said: “I’m thinking about the Ryder Cup every second of every day.”
In an earlier interview with Sports Illustrated, Bradley said he knew there was “a big risk” he would not be selected.
Thomas, who was 15th on the qualifying list, had previously had a successful pairing with his good friend Jordan Spieth, who was eighth on the list and also selected by Johnson, who was criticised after the defeat for fostering a “boys” club.
“The thing is, those guys are close. They’re not just PGA Tour-close, they’re close friends,” Bradley said.
“If you take golf out of the equation, they’re legit close friends. You have your close friends as a golfer and then you have your close PGA Tour friends, and a lot of the time your close friends aren’t on the Tour.”