The Blues’ 10-game unbeaten run came to an end against the play-off side at Fratton Park after a 2-1 reverse.
Pompey were undone on the counter twice in the first half after wasting opportunities, and then pushed after the break but could only find one goal from George Hirst despite more openings.
Cowley said: ‘We’re disappointed about the result, but there was a lot to like about the performance.
‘For the first 20 minutes we dominated against a good MK Dons - probably creating three or four good opportunities.
‘I think it’s fair for people to be critical of our final action. We need to be more clinical and ruthless in that moment.
‘They scored the first time they’d been in our half, let alone their penalty area.
‘I was disappointed with the way we responded to that.
‘You can’t play as well as we did for 20 minutes, have one moment of disappointment and let it affect you that much.
‘It’s happened a few times here when we concede. It seems to hit the players hard and we have to try to navigate through that period more effectively.
‘I thought in the second half we dominated possession and territory, something like 22 shots, got to the final third time and time again - but we lacked a bit of quality,
‘People will criticise us for that - and that’s fair.’
Pompey’s worst passage of play came after they went behind to Mo Eisa’s first-half opener, as Cowley’s side lost their way.
The Blues boss believes that response to adversity needs attention - especially when he feels it’s clear what is required.
Cowley said: ‘We know what the supporters want. You can feel it here.
‘They respond to a big tackle, a big header or when you come out with the ball in that combative moment.
‘That gets them off their seats.
‘Maybe when we do concede we need five minutes of going after those combative moments.
‘We definitely have to manage that period better.’