The East Lothian club has voted against accepting female members, losing the right to host golf’s Open Championship in the process.
The ballot was held at the end of a two-year consultation on membership but failed to get the two-thirds majority of its 648 eligible voters required to change policy.
The decision was met with outcry from key figures from the sport and beyond, with many calling on the club to look again at its membership rules.
Speaking to BBC Radio 5 Live, Mr Alliss said the issue was “a very emotive subject”.
He told the programme: “The women who are there are wives of husbands. They get all the facilities. If somebody wants to join, you’d better get married to someone who’s a member.”
Mr Alliss, 85, continued: “I believe clubs were formed years ago by people of like spirit - doctors, lawyers, accountants, bakers, butchers, whatever they like.
“And they joined in like spirit to talk amongst them and to do whatever. I want to join the WVS (Women’s Voluntary Service) but unless I have a few bits and pieces nipped away on my body I’m not going to be able to get in.”
Meanwhile, Rory McIlroy led calls from top golfers for the club to “see sense”.
He 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 (golf’s governing body) did the right thing. It’s 2016 and we have to move with the times. It’s taken long enough.”
Political leaders also weighed in on the issue on Thursday, with Scotland’s First Minister Nicola Sturgeon describing the result as “indefensible” and Prime Minister David Cameron saying it was “outdated.”’