Pitted against a determined Posh side who belied their standing at the bottom of the Championship table, the sides had gone in level at the break in a fiercely competitive fifth round encounter.
But a superb 19th goal of the season from Riyad Mahrez on the hour made the all-important breakthrough for City.
“We are in the next round and in the end, the quality of our players made the difference,” Guardiola declared.
“They were brilliant goals. The quality of Riyad and the second goal the same. It was good.
“We created chances. All of them were brilliant.
“Riyad always had this quality in the final third - he is the best we have. He scored a fantastic goal. So proud of the game he played.
“The pass from Phil (for the Grealish goal) was excellent - the control was excellent from Jack.
“He was aggressive in the final third and is back from injury and played a really good level.”
The City boss also praised the contribution and example of Oleks Zinchenko.
In the midst of a very serious situation in his Ukrainian homeland, Zinchenko was made skipper for the night.
“It’s not an easy period for Oleks. His family, his country but playing football is the best for him at the moment,” Guardiola added.