United can widen the gap to 12 points with a victory over Everton on Sunday and when asked if he was conceding the title to United Mancini said: "Maybe. 12 points is too much at this moment and we have not played well in the last two games."
The City boss added: "This is strange because we played the whole of January really well, I don't know why we played so bad today. 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."
City fell behind in just the seventh minute when Jason Puncheon tucked away the rebound from Rickie Lambert's strike. The visitors then became their own worst enemy as Steve Davis doubled the home side's lead after City goalkeeper Joe Hart allowed Lambert's shot to squirm through his hands.
Edin Dzeko reduced the arrears before half-time but a Gareth Barry own goal early in the second half secured a first win for Saints' boss Mauricio Pochettino and left Mancini ruing his side's 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."
Mancini also hit out at the midweek international programme, saying: "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. Sometimes the fixtures are ridiculous because they don't think about this but we played a bad game."
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, it has been an incredible day.
"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."