Willey was axed by Smith and the selectors despite playing a big part in England’s rise to No 1 since the last World Cup in 2015.
The 29-year-old was ultimately jettisoned in favour of rising star Jofra Archer, the Barbados-born pace bowler whom England fast-tracked by changing their residency rules from seven years to three.
Willey is now expected to return to Yorkshire duty although could yet rejoin the national squad if injury strikes in the seven-week tournament.
Willey’s omission comes as fellow Yorkshire all-rounder Tim Bresnan was yesterday diagnosed with a grade two calf tear after pulling up during last week’s County Championship match against Kent at Canterbury.
The club have put no time-frame on Bresnan’s absence, although it could be in the region of four to six weeks.
Writing on Twitter, Willey said of his World Cup blow: “What can I say, I’m absolutely gutted. Still 100 per cent behind the lads.”
Then, attaching a video of his young son dancing to music, he added: “On a positive… still winning at life!!”
Martyn Moxon, the Yorkshire director of cricket, said that everyone at the club was devastated for Willey, whose left-arm variety has been a key weapon in England’s white-ball resurgence.
“We are very disappointed and gutted for Dave,” said Moxon.
“We know how hard he’s worked and how much it would have meant to him; it would have meant a hell of a lot playing in a World Cup in England.
“A home World Cup doesn’t come around very often, so it’s obviously a big blow.
“It was clearly a very difficult decision for the selectors, and it was going to be incredibly tough on whoever missed out.”
Willey’s omission leaves Jonny Bairstow, Joe Root and Adil Rashid as Yorkshire’s representatives in a competition that starts on Thursday week when England face South Africa at The Oval.
Kent’s Joe Denly was the other man left out from the provisional squad in favour of Hampshire’s Liam Dawson, who will cover for a slight shoulder niggle to Rashid that is not expected to prevent him from starting the tournament.
Smith delivered the bad news to Willey over the phone and said that the player’s dignified reaction spoke volumes.
“I spoke to David and he was disappointed, but extremely dignified and polite,” said Smith. “Exactly what you’d expect from the kind of man that he is.
“I explained the reasons, and he took it in exactly the way that characterises this one-day side.”
Smith described it as “a very difficult decision” to leave out a player who has taken 52 wickets in 46 one-day internationals since his debut in May 2015, with a strike-rate of 37.9 and an economy rate of 5.7.
“David has been a big part of the one-day side and it was a really tough call, but someone had to miss out,” he added.
“The new ball area is strong at the moment and David was very unfortunate.
“He could easily have been in this World Cup squad, deserves to be in the World Cup squad, but that’s sport.
“Sometimes there are more deserving people than there are places in the squad.”
England have instead gone with a pace quintet of Archer, former Yorkshire player Liam Plunkett, Chris Woakes, Mark Wood and Tom Curran, with support provided by all-rounder Ben Stokes.
The inclusion of Archer comes after he was left out of the provisional party pending a trial run in games against Ireland and Pakistan.
Archer made four appearances in all as England rotated their squad for those fixtures, catching the eye with his blistering pace.
The 24-year-old, who has an English father, is expected to light up a World Cup for which England are favourites.
“He’s a very good cricketer, very talented, very exciting, has pace, bounce, athleticism and skill with the bat,” said Smith.
“He’s an outstanding talent; that was clear to all of us. He’s made a very good start to his England career, and long may that continue.”
Commenting on his call-up, Archer said: “I can’t believe it has happened to quickly. I had it in my head I’d have to wait seven years.
“I was always prepared to wait however long it would take.
“Everyone welcomed me with open arms from the moment I got in.”
Asked whether England are good enough to win the World Cup, Smith was unequivocal.
“Clearly the squad is good enough to win the World Cup,” he said.
“There are no guarantees in elite sport, we know that, but it’s a very exciting situation.”
England squad: Eoin Morgan (captain, Middlesex), Moeen Ali (Worcestershire), Jofra Archer (Sussex), Jonny Bairstow (wicketkeeper, Yorkshire), Jos Buttler (wicketkeeper, Lancashire), Tom Curran (Surrey), Liam Dawson (Hampshire), Liam Plunkett (Surrey), Adil Rashid (Yorkshire), Joe Root (Yorkshire), Jason Roy (Surrey), Ben Stokes (Durham), James Vince (Hampshire), Chris Woakes (Warwickshire), Mark Wood (Durham).