The Blues made nine changes for the third-round tie and almost trailed when Asmir Begovic saved Lee Angol's close-range header.
Terry saw red for bringing Angol down as the last man and Tom Nicholls prodded in from six yards for a buoyed Posh, only for Pedro to restore a three-goal advantage from the edge of the box.
Before his early bath Terry had completed 100% of his 30 passes, though he only won 20% of his duels, less than defensive partners Gary Cahill (50%) and the fit-again Kurt Zouma (60%).
"John played a really good game," added Conte. "For me, in this season he has shown me great ability."