Andy Burnham has claimed he would be leader of the Labour Party if leadership election rules had not been reformed.
The shadow home secretary, who bid for the leadership last year, said it was hard to accept that the changes meant he missed out on the top job.
"The MPs used to have much of the control of the nomination of the Labour leadership, but also a third of the electoral college. That's now changed," he said in an interview with The Observer's The New Review magazine.
"The vote is now a pure one member, one vote. And that's probably why I lost the last leadership election."
In 2014, the Labour Party adopted a new method for electing its leaders which scrapped the three-way electoral college system where votes were split between the unions, individual party members and the Parliamentary Labour Party (PLP).
It was replaced with a one member, one vote method whereby members directly elected the leader - although candidates still have to be nominated by at least 15% of the PLP.
Mr Burnham, who fought for the leadership against Yvette Cooper, Liz Kendall and Jeremy Corbyn last year, received 19% of the votes, compared with 59.5% for Mr Corbyn.
Despite believing the rule changes cost him the chance to lead the party, Mr Burnham said he supported party members electing the leader.
He told the magazine he found it "pretty hard" to take that if the 2010 leadership rules had been in place in 2015 then he would probably have won.
"I still think the rules are right... it being members of the party deciding."
Mr Burnham, who is standing for mayor of Greater Manchester, also said he was finished with "Westminster shenanigans" after spending 10 years in the cabinet and shadow cabinet.
He said there were facets of it that he did not like.
"There's a kind of in-built snobbery in the place. It doesn't take too well to people with accents.
"The more I've seen of this country at close quarters, in terms of the establishment, that frightens me."