The champions' failure to win any of their last three games has left them with a 12-point gap to bridge if they are to catch Manchester United in the Premier League.
Despite that faltering title defence Mancini has rubbished suggestions his job is on the line and says his critics "don't understand football".
And the first manager since 1968 to deliver City a league title does not feel under pressure from chairman Khaldoon Al Mubarak.
The 48-year-old said: "I speak with Khaldoon every week.
"He is like me. When we lose he has my mentality, he is upset and disappointed but this is normal and it's correct in football.
"After you lose you can't be happy for 24 hours but after that you need to think about the future.
"We have a good relationship. At this moment they aren't happy because when you lose you can't be happy but I think they are happy with our job over the three years."
The dismal 3-1 defeat at St Mary's has sparked fresh speculation over Mancini's future at the Etihad Stadium.
Some critics have even suggested the 48-year-old could be dismissed if npower Championship side Leeds dump City out of the FA Cup at the fifth-round stage this weekend.
In an outspoken attack, former City and England defender Danny Mills even said Mancini's successor could be appointed by Thursday if the season takes another downturn on Sunday.
But Mancini, who ended City's 35-year trophy drought in 2011 and followed up with a first league title in 44 years last season, brushed aside such suggestions.
He said: "I don't know what I should say about this. We started our project three years ago.
"We won the Premier League maybe too quickly because usually it is four or five years for a team like City to do this.
"All the people who talk about this don't understand football.
"Because if Manchester City should sack me, the other 20 teams in the Premier League should be without a manager."
Mancini reacted angrily to his side's performance at Southampton and was heavily critical of the players.
He now expects a reaction as Leeds visit.
He said: "I think that the players know they didn't do their job at Southampton and sometimes it is important they take the responsibility.
"I think that we have some players that can do better than this year but I am sure I have a good team and at the end of it we will win something.
"It will be different because it's the FA Cup but it won't change for us because results are always important and there is always pressure.
"The players will respond, I'm sure about this."
As for the title race, Mancini claims it is not in his nature to concede defeat.
He believes that if the deficit can be cut before City travel to Old Trafford on April 8, further league success remains possible.
Mancini said: "I think that is a difficult moment because we lost seven points in three games but in football sometimes it is strange.
"When you think it is finished, three or four games can change everything.
"While we have the points available to win, we should believe in ourselves.
"We play the derby in April and from now until then we have six games and we need to look at what happens in the next six games.
"If we reduce the gap before the derby... but it's not important to look at the table. It's important to win, win, win."
'We won the Premier League maybe too quickly because usually it is four or five years for a team like City to do this.' - 'Team like City'? There are no other teams like City, Roberto, and there never have been. £930m spent since 2008, two-thirds of which came straight out of a sugar daddy's pocket? Not sure I see who you're comparing yourself with mate. I sometimes take you seriously when you talk about money, transfers, etc. but then I remember that you have more millions at your disposal than most clubs have seats, but you still find reasons why things are so difficult and why City can't be expected to compete against A, B or C. If you take a billion of an oil magnate's cash, giving you ten times what most of your competitors will ever have, you better think a bit more carefully about what needs to be achieved. Spending the GDP of a Caribbean island to win two trophies, then planning a clear-out 12 months later and more astronomical spending makes you look a bit c**p in all honesty. Long may you stay at City.- big dave