Diao's stoppage time strike from close range gave Stoke all three points and pushed Portsmouth closer to relegation from the Premier League - if they survive until the end of the season.
British media reported this week that the club, which faces a winding-up order for unpaid taxes from the Government's Customs and Excise department in the High Court on March 1, has debts of more than 70 million pounds.
Saturday's result left Portsmouth stranded on 16 points from 26 matches - eight points from the safety zone.
The mood at Fratton Park turned to utter dejection after Stoke's winner in contrast to the earlier joy after Frederic Piquionne had put them ahead after 35 minutes.
Robert Huth's 50th minute equaliser for the visitors had silenced one of the noisiest sets of home supporters in the country but many were in tears at the final whistle.
"Everything is going wrong. We knew that one point for us was like getting zero points, so we wanted to win the game, then they scored from a counter-attack.
"We started the second half very well, but some of our players are not tall enough to defend set pieces and they equalised... then scored the second goal.
Earlier on Saturday, the Premier League announced it had refused the club's request to raise vital funds by selling players outside the transfer window.
Hart, analysing the match for ESPN, said: "Stoke's first goal knocked the stuffing out of them. It killed them."
