The Blues were 2-0 down by the 34th minute after defensive mistakes had allowed John Marquis and Andy Williams to score for Doncaster Rovers.
Carl Baker’s fourth goal of the season reduced the deficit shortly before half-time and also later struck the bar, but there was to be no leveller.
It represented a second successive defeat for Pompey amid some alarming errors at the back.
And Cook was frustrated with how his team began against their fellow promotion rivals.
He said: ‘If you don’t start a game that can happen.
‘The biggest quality we’ve had, in our first home games especially, has been our ability to get on the front foot quickly and to take the game to teams.
‘I felt we lost the game in the first 15 minutes, it was like we just weren’t involved in a competitive game.
‘For 20 minutes we looked everything we were, open, not aggressive, not off the front foot and found ourselves two down.
‘From there we huffed and puffed, did our best and deserved to get a point, but the reality is we lost the game.’