Kenny Jackett bemoaned Pompey’s sloppy start which inflicted a Keepmoat Stadium defeat.
The Blues found themselves 2-0 down after only six minutes, following goals from Liam Mandeville and a Christian Burgess own goal.
Mathieu Baudry’s second-half own goal gave the visitors hope of grabbing something out of the game, only for Dion Donohue’s mindless red card to deflate the momentum.
Ultimately, Doncaster ran out 2-1 winners – and Pompey’s boss pinpointed the wretched start as laying the costly foundations.
He said: ‘Our start was poor, we got it wrong.
‘Tommy Rowe has gone past our right-back and central-midfield players too easily on the edge of the box and slotted somebody in for the first goal.
‘Then they have had two other chances straight away from corners, where Rowe and then Joe Wright have got the first headers – one resulting in an own goal from Burgess and the other hit their player on the line.
‘They have had three clear-cut chances in those five minutes, which is disappointing from our team and our set-up.
‘After that I wasn’t disappointed with the way the players played.
‘There were some key moments such as Burgess’ header from a set-piece and Conor Chaplin’s free-kick which hit the post, while their keeper saved at the end from Jamal Lowe’s header.
‘We went down to 10 men and kept going and still made a good fist of it and showed a good attitude.’