And even worse was to follow as the North End stopper allowed a 25-yard McCann shot to slip through his hands after 29 minutes.
Rudd did atone for his errors with terrific saves from Paul Taylor and Barnett, but those goals were enough to ensure Posh closed to within a point of top spot and won eight of their opening 10 league games for the first time in their history.
Grayson said: "We can't be critical of Declan because he has been fantastic since coming to the club.
"The sign of a good goalkeeper is responding well to mistakes and he did that with some great saves.
"Our unbeaten run was always going to end somewhere and you can't get away with giving a team of Peterborough's quality a two-goal start.
"I asked the players for a reaction at half-time and got it. They could either have buried their heads in the sand or come out fighting - and they did the latter.
"We controlled possession in the second half, we hit the crossbar a couple of times, we feel we should have had a penalty and we came close to getting something from the game."