The lower-ranked Southern League division one south hosts scored the only goal of the tie with the last kick of the game.
And Borough boss Molyneaux was devastated.
‘The players saw a side of me they have not seen before,’ he said.
‘I let them have it afterwards. It was justified and necessary.
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‘It was a gutless performance and one I won’t tolerate
‘They have to realise it is my job on the line.
‘Not enough of the players realised that or the importance of staying in the FA Cup.
‘Sadly when players drop down a level they seem to rely on others to do the work.
‘Everyone needs to be held accountable for their actions and I need a lot more from them.
‘They have to make a reaction or I will be forced to take action.
‘If players don’t pull their weight then I will get others in who will.’
In the first half Charlie Kennedy forced a good reaction save from the Cirencester keeper.
Defences remained on top after the break, though, with the best opportunities continuing to fall to Borough.
Kennedy, Liam Robinson and Matt Paterson all went close, while the latter twice missed the target in the final 10 minutes.
With a replay looking odds-on, Cirencester hit Borough with a sucker-punch.
The one player to escape the manager’s post-match wrath was Josh Huggins, who replaced Richie Whittingham at half-time.
‘I think it was the only shot they had all game,’ added Molyneaux.
‘Ryan Woodford got back and made a block but our goalkeeper had already committed himself and the ball deflected past him.
‘We only had time to kick-off before the final whistle.
‘Josh was one player who showed great determination and desire to win.
‘If some of the others could add the same qualities to their ability then we can become a force to be reckoned with.’