Rory McIlroy has urged Muirfield to “see some sense” and reconsider its membership policy after the club was dropped from the British Open rota.

After a vote on accepting women members narrowly failed to achieve the two-thirds majority required, the R&A announced that the Scottish course would no longer be considered to host the game’s oldest Major championship.

McIlroy, who won the Claret Jug at Hoylake in 2014, said: “They can do what they want but in this day and age it’s not right to host the world’s biggest tournament at a place that does not allow women to become members. Hopefully they can see some sense and we can get it back there one day.

“The R&A did the right thing. It’s 2016 and we have to move with the times. It’s taken long enough. Even the R&A only started letting women join last year or whatever it was (2014). It’s about time that they did.

“Bigger picture, it’s a great golf course, but there’s so many other great golf courses that we play on the Open rota that we’re not going to miss one. I think it’s more their loss than it is the R&A’s or our loss. If that’s what they want to do, obviously it’s a free world and they can do that. But they must have known that it was going to cause this sort of controversy.”

Muirfield has staged the British Open 16 times and produced a who’s who of champions, including Gary Player, Jack Nicklaus, Lee Trevino, Tom Watson, Nick Faldo (twice), Ernie Els and Phil Mickelson.

Player echoed McIlroy’s sentiments, writing on Twitter: “As much as I love and respect Muirfield as a club where I won the Open, I totally agree with the R&A that staging the championship at any venue that does not admit women is simply unacceptable.

“I hope Muirfield will reconsider their position soon and continue hosting one of the world’s greatest golf events.”

Of the 648 members who were eligible to vote, 616 took part with 397 voting in favour and 219 against. A total of 411 yes votes was required.

Catriona Matthew, who won the Women’s British Open in 2009 at Royal Lytham and lives only a few miles from Muirfield in North Berwick, tweeted: “Embarrassed to be a Scottish women golfer from East Lothian after that decision.”

And Thomas Bjorn, chairman of the European Tour’s tournament players’ committee, was left in disbelief by the vote.

“It’s a shame that one of the best golf courses in the world is off the Open rota. I’m gobsmacked,” Bjorn said.

The announcement was also greeted with anger by those outside the game, with Scotland’s first minister Nicola Sturgeon one of the first to express her disapproval.

Sturgeon wrote on Twitter: “Scotland has women leaders in every walk of life. It is 2016. This is simply indefensible.”

British minister for sport David Evennett said: “It is an extremely disappointing decision from the members of Muirfield. We want to encourage more women to get involved in sport and this sends out completely the wrong message.”

Royal Troon is the only remaining British Open venue that retains a male-only membership and will host this year’s tournament in July. The club is currently reviewing its membership policy with a decision expected towards the end of the year.

Ruth Holdaway, the chief executive of the Women In Sport charity, described Muirfield’s decision as “ridiculous” and called for current members to protest by ending their affiliation with the club.

“In this day and age it’s completely ridiculous and it’s also commercially a really bad decision.”

The Royal and Ancient Golf Club at St Andrews chose in 2014 to admit female members for the first time in 260 years and Royal St George’s in Kent also changed its male-only policy last year.

Henry Fairweather, captain of the Honourable Company of Edinburgh Golfers (HCEG), which owns and runs Muirfield, said policy is decided by the club’s members.

“The Honourable Company is a members’ club, and, as such, the members decide the rules of the club, including its membership policy,” Fairweather said. “Women will continue to be welcome at Muirfield on the course and in the clubhouse as guests and visitors, as they have been for many years.”

R&A chief executive Martin Slumbers said in a statement: “The R&A has considered today’s decision with respect to The Open Championship. The Open is one of the world’s great sporting events and going forward we will not stage the Championship at a venue that does not admit women as members.

“Given the schedule for staging The Open, it would be some years before Muirfield would have been considered to host the Championship again. If the policy at the club should change we would reconsider Muirfield as a venue for The Open in future.”