The Black Cats carved out a number of opportunities in a goalless first half before eventually taking the lead through Kenwyne Jones in the 59th minute.
John Utaka quickly equalised and Pompey then took the lead when an Anton Ferdinand gaffe led to Phil Bardsley scoring an own goal after 68 minutes.
Armand Traore fired home a third for Portsmouth to leave Sunderland facing an anxious final day of the season.
They are still not safe from relegation ahead of their clash with Chelsea, and Sbragia admits the players were disheartened following defeat in such a crucial game.
"I thought the first goal was a bit unlucky but the second goal was a bad error and that killed us off," said Sbragia.
Punished"Anton tried to control the ball with the sole of his boot. He is better than that.
"I thought in the first half we did reasonably well and created a few chances but it was the same old story, we didn't finish them.
"We went 1-0 up and really we should try and see the game off but we didn't do that.
"The boys are down. We came here and thought we had the chance to get something. We created chances but didn't take them and they come back to punish you."