Pompey created a host of chances, but suffered a narrow defeat at MK Dons to dent their play-off aspirations.
Scott Fraser netted the game's only goal from the penalty spot after Charlie Daniels had been penalised for a trip on Ethan Laird.
Danny Cowley's side had plenty of chances, with John Marquis and Ronan Curtis both going close during an end-to-end opening 45 minutes.