Premier League leaders Manchester United can extend their advantage over second-placed City to 12 points with 12 games left if they win at home to Everton on Sunday.
City made up eight points with six matches left last term to beat United to the title on goal difference.
"Now we have 10 percent (chance) maybe. I don't think United believe that we can recover 12 points," the Italian told ESPN.
"They (Southampton) deserved to win. We didn't play well, we conceded a goal that I have never seen in my life."
Barry's own goal, which made it 3-1 and gave Mauricio Pochettino his first win for 15th-placed Southampton, was as strange as they come, with the midfielder passing an innocuous ball across the box into the net with Joe Hart beaten.
Goalkeeper Hart had dropped his own clanger for the second goal when Rickie Lambert's shot somehow went through his defences for Steven Davis to prod in.
Southampton, who upset fans by sacking popular coach Nigel Adkins last month, had gone ahead through Jason Puncheon after City's midfield and makeshift defence again looked lax.
Usual centre backs Vincent Kompany and Matija Nastasic were out injured while striker Carlos Tevez was missing due to family reasons.
"I think they understand that they played really bad. Worst game in two or three years maybe," Mancini added.
"Clearly we are missing Vinny, Nastasic and we have some players that are not in good form, play really bad without strength and personality."
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