Birmingham boss Chris Davies has enjoyed an unbelievable first season in management, winning the league title with six games to spare.
But the 40-year-old said they had to "learn" from days like this.
"It wasn't to be our day – congratulations to Peterborough – they scored two fantastic goals," he told BBC Sport.
"We got to the final third consistently but it's how do you create chances from that?
"We just couldn't find gaps in their defence.
"We started to play a bit more after the free-kick and you think we're looking strong and can kick on but then they score right on half-time.
"I think over the course of the game we were the better team – they hit two worldies from outside the box but didn't do much else.
"What today goes to show is what can happen in football – you can have days like this home and away – but to win a league title with six games to go shows how consistent we have been and things like today can happen, unfortunately it's happened in a cup final.
"Sometimes you get a punch in the face – we have to learn from days like this.
"We've still got six games to go, within that there is a day I will savour where we will lift a trophy. What I want is performances and results we can be proud of.
"It's been a bizarre weekend but once we take a step back it's one we can reflect on."