The normally placid boss was speaking in the aftermath of the Bankies losing 1-0 to Arthurlie courtesy of a 77th-minute strike from Ryan McGregor.
And Budgie wasn't shy in hiding his upset after he felt his men were denied a clear penalty after 52 minutes at Holm Park. Marauding full-back Chris Wilson had raced into the Lie penalty where he appeared to be fouled by a despairing challenge from backtracking striker Stevie Dymock, with Wilson being booked for simulation.
The Clydebank boss said: "Why anyone would think Chris would go down when he had a clear shot at goal is totally beyond me.
"And it's of little consolation that Stevie spoke with me afterwards and admitted to catching Chris because we now find ourselves out of the cup when a penalty could have seen things turn out so differently.
"This is no referee-bashing exercise because apart from that incident I felt he had a smashing game, but he definitely called that one wrong.
"The referee might think it appropriate to come out and admit it but I'm not holding my breath."
A virus had denied Budgie the services of top scorer Ross McPherson and little was seen of them as an attacking force in the early stages, with Lie midfielder McGregor showing them how it's done after clipping the ball beyond keeper Robert Hamilton.
He said: "Initially my thought was to go round the keeper but he never budged an inch. The ball took an eternity to cross the line but thankfully it went in."
Arthurlie manager Mark Cameron added: "It was no classic but I would put that down to both sides being ring-rusty on account of not having played in weeks."
Cameron's men were joined in the last 16 by Petershill for whom Paul Woods netted a hat-trick in a comprehensive 3-0 defeat of his former club Lanark United.
Beith similarly cruised through with a 6-1 crushing of Annbank United, but fellow top-flight club Shotts Bon Accord encountered a much tougher time away to Super First Division outfit Kilbirnie Ladeside.
The Ayrshiremen twice led only to be pegged back each time for a 2-2 draw, with Shotts winning a tense shoot-out 4-3.
Forth Wanderers had no such luck after mounting a stirring second-half comeback away to Rutherglen Glencairn to level the tie at 2-2, eventually going down 5-4 in spot kicks.
Saltcoats Vics also clinched a spot thanks to legendary ex-Auchinleck Talbot skipper Bryan Slaven bagging a brace in a 2-1 win at home to Darvel.
Meanwhile, Slaven's former club joined Petershill atop the Super Premier pile after Mick McCann and Colin Spence were on target to bring about a 2-0 defeat of reigning champions Irvine Meadow.
Pollok climbed into fifth after defeating Rob Roy 2-1 at Adamslie Park, while Glenafton were another big mover after easing themselves clear of the basement thanks to a 1-0 win over Cumnock.
Elsewhere, Renfrew recorded a 2-0 victory over Whitletts Vics and Yoker defeated Glasgow Perthshire 1-0.