A first-half strike from Harry Leonard was enough for the League One strugglers to eliminate the Bluebirds in round one – just four days after Cardiff had reached the Carabao Cup quarter-finals.
It means after starting the season with no defeats in their first 10 matches, Barry-Murphy’s side have lost five of their second 10.
Cardiff enjoyed more of the ball after the break but struggled to turn possession into chances, failing to seriously test Peterborough goalkeeper Alex Bass.
The result marks the first time since 1994 that Cardiff have exited the FA Cup at the opening stage.
Barry-Murphy admitted his side had not reached the levels they displayed in midweek and stressed the need for improved, regular performance levels.
“Obviously we wanted to progress as far as we wanted in the competition and today we weren't good enough to get that job done,” said Barry-Murphy.
“We treat every competition with the upmost importance, we want to create a mentality in the dressing room where we try to give our supporters performances they enjoy every time. Today we weren't able to do that.
“We didn't create the chances we wanted to or with the intensity in the first half we were looking for. We never reached those heights during the course of the game.
“The challenge for the players is to become more consistent, but today we did not reach the standards which we have set.
“We’re looking to be a team that is very aggressive and who play with a high level of intensity throughout the course of all the games, like we did at Wrexham on Tuesday night.
“We didn’t reach those heights throughout the course of the game.
“The challenge for the players is to become more consistent in the way that we play. It’s a disappointing day for us, but there could be beneficial learnings in terms of what we need to do better to compete in every single game.
“That’s what we’ll be working on this week with all eyes on Blackpool next Saturday.”
Barry-Murphy made four changes to the side that beat Wrexham in the EFL Cup earlier in the week, while Peterborough counterpart Luke Williams – the former Swansea City boss - also rotated his squad for what was his first game in charge of the club.
The home side made a lively start at London Road, with Kyrell Lisbie setting up Leonard for a golden opportunity inside the first minute, only for the striker to fire over from close range. Cardiff had their best opening when Callum Robinson pounced on a poor clearance from Bass, but his shot went straight at the goalkeeper.
Peterborough’s breakthrough came six minutes before half-time. Jimmy-Jay Morgan’s driven effort was deflected into Leonard’s path, and this time the forward made no mistake, slotting beyond Nathan Trott to claim his first goal for the club.
For Williams, it was a memorable start to his tenure — and a winning return against familiar opposition, having previously triumphed over Cardiff while in charge of Swansea.
“I'm so pleased with the application of the players, they showed a real warrior spirit and fight,” said Williams.
“Against top, top opposition, I'm really happy with the fight and application.
“Today they knew they would have to fight and show the fans that they still have the energy, enthusiasm and desire and today that was enough to get the victory.
“I wanted us to be aggressive and try to put balls into the box, even if we don't score it creates energy. We gave the feeling to the fans that we were on the front foot, and a lot of players put their hands up.”
The defeat was Barry-Murphy’s third visit to London Road as a manager and his third loss.
