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The pair have been friends since their teens but had a disagreement during April's RBC Heritage event, with Willett eventually missing the cut.
Smart felt mistreated and left his role, "effectively sacking" Willett, 29, mid-tournament, according to BBC golf correspondent Iain Carter.
"Things are a bit stale and kind of fizzled out," Willett told BBC Sport.
"It is a shame. But things happen and change, everything happens for a reason.
"We are still working hard to get the game in shape to get back playing the golf we know we can play."
Willett did not rule out the prospect of his childhood friend one day returning to his bag but he was forced to use a member of his management team in the second round at the RBC Heritage.
He will use Sam Haywood at this week's Players Championship in Florida. Haywood was best man at Willett's wedding and has recently been on the bag of American player David Lipsky.
"Sam knows my game really well," Willett added. "We've played a lot of golf together over the last 10 or 15 years. It's nice having someone who you can speak frankly with. He knows where my game is and when it's good. I think it's going to be good."
Smart and Willett memorably embraced in the recorders' room at last year's Masters when it became clear the Englishman had won a first major.
But he has not won a tournament since, placing outside the top-25 in the three other majors in 2016 before missing the cut on his return to Augusta in April.
The dip in form has seen him fall 10 places to 21 in the world since the turn of the year.
BBC golf correspondent Iain Carter
It's been a struggle to adjust to the status of a major champion for Willett. Results haven't been good for a year.
Recently he's missed three of the last four cuts, so these are trying times.
It came home for me today as I remember this day last year I approached him at his first tournament since winning the Masters. Now, the mood music could not be any different.

Gerald Sunnie received cheques worth tens of thousands of pounds from three pensioners.
He then forwarded the money to "individuals across Europe" while keeping a share of the cash.
He was convicted of a £33,000 money laundering charge under the Proceeds of Crime Act.
Dundee Sheriff Court heard that Sunnie initially became involved after being "deluded" into thinking that he had won a £200,000 American lottery prize that had not turned up.
Sunnie started taking in cheques that he was told were to cover "European tax liabilities" on his winnings, passing the money on after taking his portion of it.
The 58-year-old's bank accounts were closed down due to "fraudulent activity" and he was twice told by Trading Standards officers that he was helping to facilitate an international fraud.
But he started up his activity again in August 2013, taking in dozens of cheques from three elderly victims over the course of the next year.
He told his trial that a man from the fraudsters he was passing the money to had called him two weeks earlier saying his £200,000 winnings were still on the way, and that he still expected a cheque to come through his door.
Sunnie's lawyer Gary McIlravey admitted that his client was "deluded".
Depute fiscal Muhammad Sadiq, prosecuting, said: "It's clear he may have been a victim at first, but he did then benefit by processing payments on numerous occasions after being told it was a scam."
Sheriff Simon Collins QC convicted Sunnie of money laundering, saying a large number of vulnerable people had been defrauded out of a large sum of money.
The sheriff added: "By any standard the arrangement he entered, even from the outset, was obviously a scam.
"He was told it was a scam and that he was taking part in a fraud and his bank accounts were closed.
"He processed nearly £52,000 but claimed not to have made even inquiries of those involved in these arrangements. This stretches credulity."
He said Sunnie's role had been "key" to the scam, that his motivation was "clearly personal gain" and that he had shown "little or no remorse".
Danny Willett has split with caddie Jonathan Smart just over a year after winning the Masters at Augusta.
[NEXT_CONCEPT]
A "deluded" money launderer who helped run a lottery scam that targeted elderly victims has been jailed for six months.