Inexplicable mistakes by Joe Hart and Gareth Barry helped Saints achieve their first win under Mauricio Pochettino in style.
Hart could have possibly done better with the shot that led to Jason Puncheon's opener, and there was no doubting the England goalkeeper's culpability for Steven Davis' bundled second goal for the hosts.
Edin Dzeko reduced the deficit as half-time approached, but soon after the break Southampton's two-goal cushion was restored as Barry passed into his own goal unchallenged.
"I am disappointed with our performance. They deserved to win," Mancini said on ESPN.
"We didn't play well. We conceded a goal that I have never seen in my life. That's it. Now we can do nothing - only say congratulations to Southampton for their performance.
Asked if it was a poor performance Mancini replied: "No, I don't agree, it was worse than poor.
"We didn't play. We played with maybe two players in this game and with 11 against two it is difficult to win.
"I think (the players) understand that we played really bad. I think it's the worst game in the last two or three years, maybe.
"We're missing Vinny (Kompany) and missing (Matija) Nastasic, and we have some players who are not in form. They played really bad - without strength, without personality. I'm very disappointed in them."
When asked if he was conceding the title to United Mancini said: "We have 10 per cent, maybe.
"12 points is too much at this moment and we have not played well in the last two games.
"This is strange because we played the whole of January really well, I don't know why we played so bad today [Saturday].
"Southampton are playing well and it is difficult to score against them - I don't think a team like us can do a performance like today [Saturday]."
Mancini also hit out at the midweek international programme and believes a number of his players returned to City's Carrington training base looking jaded.
All of the players came back Thursday night or Friday and when you have 16 players away on international duty it is difficult to prepare," he said.
"Sometimes the fixtures are ridiculous because they don't think about this but we played a bad game."
City are now an outside bet to retain the Premier League crown they secured in such extraordinary standards on the final day of last season and Mancini thinks he knows what is to blame.
"We need to work more," he said.
"Probably we think that, because we won last year, we are top players but if you want to stay on the top for a long time you have to work always and forget what you did last year."
Pochettino dedicated his first win since replacing Nigel Adkins last month to everyone involved with Southampton.
"I'm very proud and very happy for the team, who deserved the victory," he said.
"I'm very happy for all the people who work with Southampton and for all the people here at St Mary's today [Saturday], it has been an incredible day."
The Argentinian also felt his side were fully deserving of the three points and restricted City playing their natural game.
"I have seen that we cut the connection between their lines and have not let them play," he said.
"It (the result) has a great value. The team has deserved its victory not least because of the three goals scored against Man City."
With all eyes on the top of the table it will not have slipped Pochettino's attention that Saints are now six points clear of the bottom three.
Southampton striker Rickie Lambert felt his team were worthy winners against the defending champions.
"I think it's our best performance (of the season)," he said on ESPN. "We were absolutely superb today [Saturday] and got exactly what we deserved.
"We looked for the early goal and looked to put them under pressure early and hope to capitalise on it. It worked perfectly. Then we went 2-0 up, which was even better."
The margin of victory could have been even greater had referee Martin Atkinson not waved away Jay Rodriguez's penalty appeals on the stroke of half-time.
Man of the match Rodriguez said: "I ran in and I think there was a little nudge, but the referee hasn't given it so we got on with the game."
He added: "We press hard, take the game to them. As you can see, it creates chances and puts us on the front foot. We've taken to it well and put in a great performance."