Pompey spent most of the second half at Fratton Park trying to batter the Peterborough door down.
Christian Saydee had already cancelled out David Ajiboye’s opener in the Carabao Cup second round contest.
The visitors then had Charlie O’Connell sent off for a second bookable offence and were left hanging on.
But they eventually triumphed 5-4 on penalties to progress and John Mousinho felt that Pompey’s performance in the first half was the cause for their exit.
The Blues boss said: “We’re obviously disappointed not to be in the hat for the next round of the competition.
“To be really clichéd, it was a game of two halves and we looked a bit lethargic and tepid before the break.
"The message to the lads is that you can’t wait for things to happen and for some choice words to spark you into life."
“But we were completely different afterwards and it was like watching a different team – we were at it from the start.
“So the message to the lads is that you can’t wait for things to happen and for some choice words to spark you into life.
“I thought we deserved to win for the way we played in the second half and we were a penalty away from doing just that.
“There were plenty of near misses and we do need to be better in those areas in order to finish teams off.”
Saydee controlled Paddy Lane’s cross on his chest and hooked the ball home to open his Pompey account.
Mousinho said: “I’m really pleased for Christian and thought he was excellent – he was a constant thorn in Peterborough’s side.
“He put a real shift in and that’s the first time he’s completed 90 minutes for us, while he took the goal well.”