Rory McIlroy has led calls from top golfers urging Muirfield to "see sense" after the club was stopped from hosting future Open Championships for refusing to accept women members.
The Scottish club's vote to change its rules and allow women fell short of the required two-thirds majority.
Governing body the R&A responded with its ban on Muirfield hosting The Open until the club changed its rules.
"It's more of a loss to Muirfield than it is to us," said McIlroy, 27.
The world number three added: "It's not right to host the world's biggest tournament at a place that does not allow women to be members. Hopefully Muirfield can see some sense and we can get it back on The Open rota."
McIlroy's view was echoed by Gary Player, who has won nine majors, including The Open at Muirfield in 1959.
"As much as I love and respect Muirfield as a club where I won The Open, I totally agree with the R&A," said the South African. "Staging the championship at any venue that does not admit women is simply unacceptable."
In announcing the club's decision, Muirfield captain Henry Fairweather stressed that women will continue to be welcome at the East Lothian club as guests and visitors, "as they have been for many years".
Veteran BBC golf commentator Peter Alliss said women who want to play at Muirfield should "marry a member" in order to play.
He also said he had spoken to the wives of Muirfield members and claimed there was "a look of horror" on their faces when he suggested they might be able to become members in their own right.
He reckoned they did not want to become members because they would have to start paying for something they currently got for free.
"The women who are there as wives of husbands, they get all the facilities," he told BBC Radio 5 live. "If somebody wants to join, well you'd better get married to somebody who's a member."
Alliss, 85, said he understood why members had failed to vote in large enough numbers to overturn the ban on women members.
"Clubs were formed years ago by people of like spirit - doctors, lawyers, accountants, bakers, butchers - and they joined in like spirit to talk amongst themselves and do whatever," he said.
"I want to join the Women's Voluntary Service, but unless I have pieces snipped away from my whatever, I'm not going to be able to get in."
Scotland's First Minister Nicola Sturgeon said Muirfield's stance was "simply indefensible", while Women's Open winner Catriona Matthew said she was "embarrassed to be a Scottish woman golfer from East Lothian".
Ivan Khodabakhsh, chief executive of the Ladies' European Tour, said Muirfield's decision had left him "speechless".
Speaking to Radio 5 Live's Breakfast programme, he said: "The decision is appalling. We are in the 21st century and we are talking about criteria which discriminate based on gender.
"I thought these things were left behind us in the late 19th century."
Like McIlroy, Europe's Ryder Cup captain Darren Clarke - a former Open winner - said he hoped Muirfield would rethink its decision.
"Muirfield have chosen to go their path - and fair play to them - but from a professional golfer's point of view it's disappointing that we will not be playing Muirfield in the foreseeable future," he said.
Graeme McDowell said he was "disappointed" with Muirfeld's stance.
"I completely understand the R&A's decision," he said. "This is an equal opportunity world, we're trying to grow the game.
"Muirfield are well within their rights to make that decision - a private club is a private club - but we're very disappointed to lose them."