The Blades were good value for their victory, courtesy of second-half goals from Billy Sharp and Callum Morton (own goal).
Posh had a good chance of their own in the first half, when Jonson Clarke-Harris went through one-on-one but saw his shot saved by Wes Foderingham.
Posh fans were unhappy in the second half, with some chanting ‘Fergie, sort it out’ in the direction of their manager.
And Ferguson said afterwards: “It was always going to be a tough game for us, playing against a very, very good opposition.
“But we got to half time nil-nil and said: ‘Don’t give them anything cheap’. We had to make sure we looked after the ball. The goals were given away; they were so avoidable.
“This league is unforgiving and you can’t let Billy Sharp have a chance because it’s a goal. Both were avoidable and when we had moments and chances - and we had a big one with Jonson - these are ones we have to take.
“It can be difficult at times because they dominated a lot of the ball and when we had chances to counter-attack, we made the wrong decision.
“That’s what we’ve got to do better. If you do go ahead then the game will open more. But they give everything, we just can’t seem to find a way to keep a clean sheet and some of the defending was very naïve.
“We have to sort that out.”