The Scottish champions wanted a ballot held to decide which of the two last-four clashes should be moved to the rugby stadium.
They described the failure to do this as both “irrational and discriminatory”.
The Scottish Professional Football League confirmed the switch on Wednesday evening, with Murrayfield staging the Hearts-Celtic game at 1.30pm on 28 October, while the Rangers-Aberdeen clash remains at Hampden on the same day but with a later kick-off time of 4.30pm.
A spokesman for the SPFL said: “In reaching our decision, we have consulted with Hampden Park, the Scottish FA, Scottish Rugby, Police Scotland, Transport Scotland via the Scottish Government and with the four clubs involved.”
However, Celtic are unimpressed and released a lengthy statement condemning the decision.
“The SPFL Board’s decision not to hold a ballot to decide the venues of the forthcoming semi-final matches is both irrational and discriminatory,” said the statement.
“Celtic recognised there was a genuinely difficult problem to resolve. All we asked for was equity of treatment – in other words, a simple ballot of which game went to which venue, so that all clubs would have a 50-50 chance of playing at Hampden.
“We understand that those bodies consulted, including the police and broadcasters, had no preference whatsoever on which match should take place at each venue and, therefore, there was only one appropriate method of reaching a fair outcome.
“The SPFL Board have been unable to produce logic or reason for turning down our modest request. Instead, they have arbitrarily decided that a chosen game should stay at Hampden and the other should go to Murrayfield.
“The interests of our club and supporters have been subordinated to a diktat from the SPFL board which is as unfair as it was unnecessary.
“Celtic Chief Executive Peter Lawwell was excused from the SPFL board meeting due to the subject under discussion.”
Both ties were originally scheduled to be played at Hampden on the same day. But this plan was criticised by Hearts, Aberdeen, politicians, police federation officials and ScotRail, who said there had been a lack of consultation over the transport implications.