A double from James Hanson on his 300th display for City, along with efforts from Kyel Reid and substitute Steven Davies, saw a dominant display from Parkinson's men rewarded with three much-deserved points at the ABAX Stadium.
Parkinson said: "It was a terrific response from the lads after last weekend (the defeat vs Burton Albion). They implemented everything we had asked them to do on the training ground.
"There was a lot of outstanding individual performances out there - you could make a case for a lot of them to be man of the match.
"The discipline and team work-ethic was excellent, and our quality on the ball in possession was excellent - a big improvement on last Saturday.
"Big James (Hanson) was outstanding and he was a threat all afternoon. He was practically unplayable today (Saturday) - they couldn't handle him.
"Reidy produced probably his best performance of the season. That is all credit to (Head Physio) Matt Barrass though.
"We know that when Kyel is happy, he can produce his best performances. Matty has been working hard with Kyel to get his knee right.
"We decided as a group of staff to take him out of the firing line a bit for the last couple of games to clear up his (knee) problem, and he was great this afternoon.
"Ben (Williams) and all of the back four were brilliant as well.
"The blocks, the saves, the defending one-on-one was really good. Clean sheets are important, and they had to earn that one because Peterborough have so many good attacking players."
On his first ever start in senior football, debutant Josh Cullen impressed in midfield alongside the returning Lee Evans after the 19 year-old signed on loan from West Ham United on Thursday.
Parkinson added: "He played great but we knew he was capable of that from what we had seen of him in training.
"Josh and Lee (Evans) played with great calmness and control in that midfield - they made a difference to the team.
"That bit of class on the ball when we won it back was important, and it was a good performance from both of them."