Stenhousemuir 4-2 Falkirk: VIDEO Managers' reaction
The Bairns took the lead through Paul Paton, but a double from youngster Conor McBrearty turned the game in the Warriors' favour.
Joe McKee levelled things up before the break but Falkirk's "abysmal" defending cost them dear as Sean Dickson and Mark McGuigan made them pay in the second half with two further strikes to send the Warriors through to round four where they will face Aberdeen.
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Hide AdMcKinnon said: "I'm very, very disappointed. It's hard for me to take and it is hard for me to watch that. We just didn't have the quality it is as simple as that - to win games you need to have quality all over the park and we lacked that massively.
"I'm gutted for fans, there were 1500 here and they deserve better than that.
"That's really poor from us and we deserved what we got. We need to improve as a team and we're not making any excuses that's just not good enough. Fair play to Stenhousemuir they beat us fair and square.
"We actually thought we were Barcelona in the first half trying to take it out and play but we're not that good.
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Hide Ad"We need to stick to what we are good at and that is being competitive and aggressive. We didn't do that and we got punished for it and we thoroughly deserved to get beat.
"We're not hiding away from it and we need to bounce back at Inverness. We hope we can keep our run going in the league."
Caretaker boss Colin McMenamin hopes the victory has boosted his chances of securing the job on a permanent basis.
He said: "I've been told I'm getting at free drink at the wee bar and at this club that is something to shout about.
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Hide Ad"I made it clear I want to be considered for it and we'll see how it goes.
"Hopefully I've given them a decision to make. I've got this club at heart I've been here four or five years now and I've loved every minute of it and I want to be around to help them grow.
"I've lost the two before that so I don't know if it makes much of a difference. I can only do what I'm asked to do by the board and I do that to the best of my ability.
"I try to prepare the team right. I did my research, I knew how Falkirk were going to play and I'll just see what the board will say.