Media playback is not supported on this device
The Black Cats suffered their heaviest Premier League loss, and biggest defeat in 32 years, in the game at St Mary's.
"It's the most embarrassing time I've had on a football pitch. I cannot watch it again," said Poyet, 46.
"I learned a lot about the players - the bad side as some gave up and I know who they are for the future. I feel very sorry for the fans."
Poyet said he may tell his players to watch a recording of the game, and expects a reaction from them when they face Arsenal next Saturday.
"Maybe the players will watch it. Maybe it will be good therapy for them to watch themselves," said the Uruguayan.
"It's going to be a difficult week. The players who are on the pitch next week are going to do something about it."
Media playback is not supported on this device
Match of the Day pundit and former Southampton striker Alan Shearer said: "Southampton were brilliant but they were allowed to play. Sunderland were absolutely woeful. Embarrassing. And the players downed tools far too early for anyone's liking.
"Players weren't chasing back, they were turning their backs on the ball and it was so sloppy it was incredible. I'll be fascinated to see Gus Poyet's team next week because he could leave any of them out."
Sunderland scored two own goals in the defeat, including a spectacular volley from Santiago Vergini, whose attempted clearance flew past keeper Vito Mannone.
The points were all but sealed at half-time thanks to the own goal and close-range efforts from Graziano Pelle and Jack Cork.
But the hosts added five more goals in the second half to complete the rout for Ronald Koeman's men.
Despite the margin of victory, the Southampton boss felt his side have room for improvement.
"That 8-0 is not a normal result," said the Dutchman. "I was surprised after 20 minutes about the score. We were 2-0 up and we didn't start the game well. Sunderland were dominating and we had problems.
"Lucky the first one, the own goal, gave us a little bit more confidence and we woke up after that."
Shearer said: "Ronald Koeman deserves a tremendous amount of credit because the players have gelled very quickly."
Sunderland manager Gus Poyet says his side's 8-0 defeat at Southampton is his "most embarrassing" moment in football.