A solitary second-half strike from Britt Assombalonga earned them victory against League Two side Dagenham & Redbridge at London Road.
Assombalonga was perfectly placed to convert a cut-back from strike-partner Nathaniel Mendez-Laing in the 57th minute as Posh moved to within three matches of Wembley.
The goal arrived seconds after the Daggers had squandered a glorious chance of their own as Abu Ogogo headed over a terrific Gavin Hoyte cross from close range.
Posh goalkeeper Bobby Olejnik also had a lucky escape when his clearance thumped against Daggers frontman Chris Dickson and ricocheted into the side-netting.
Posh had earlier been denied an opening goal by the woodwork. Veteran midfielder Grant McCann crashed a free-kick against the crossbar during the final action of the opening period.
Impressive defender Shaun Brisley also fired into the side-netting but Posh didn't pose enough of a threat for their manager's liking.
Ferguson said: "We haven't killed teams off often enough this season and this was another example of that.
"We are getting so many good opportunities in the final third but we have not taken full advantage of them.
"We know that is an area we need to improve on and it is something we will aim to do on the training pitch.
"Our defensive record is excellent and we are good at getting control of a game in midfield but we are not quite there up top.
"We did enough to win the game, though, and I selected what I felt was my strongest team because we are taking this competition very seriously."