London Road was packed with more than 13,000 fans for the clash between the local rivals but the home supporters had little to cheer as Norwich dominated despite making eight changes to the side beaten by West Ham on Tuesday.
Elliott Bennett opened the scoring in the 30th minute and Simeon Jackson added a second four minutes before half-time.
The expected challenge from Posh never really materialised, with the excellent Robert Snodgrass grabbing a third in the 70th minute, and Ferguson did not mince his words about his side's display.
He said: "We've got our largest crowd of the season and I have to apologise to my own supporters for that performance because we're at home in a cup game which my players, for whatever reason, turned into a pre-season game.
"I'm quite glad it's taken me a while to talk to the press, and I haven't had a meeting with the players yet, because sometimes you can say things you might end up regretting.
"It was a shocking performance. If you've got your first proper tackle after 65 minutes in a cup tie then you're going to lose.
"I can accept people playing badly but the most disappointing thing for me was Norwich looked like they wanted it more, and they were the ones that made a lot of changes.
"I know what I'm going to say to the players. They'll expect me to pick them up again and perhaps they're starting to take that for granted."