A morale-sapping 3-1 defeat at Southampton last weekend left champions City 12 points behind Manchester United in the title race and the FA Cup is now the only silverware realistically still in the club's sights this season.
"All the people who talk about this don't understand football," Mancini, whose side finished bottom of their Champions League group, told reporters when asked if he was worried about getting the sack.
"If Manchester City should sack me, the other 20 teams in the Premier League should be without a manager."
Mancini led City to their first English title since 1968 last season, having won the FA Cup a year before that for the first time since 1969.
Things have not gone to plan this season, however, and defeat at home to Championship (second tier) side Leeds on Sunday would turn up the heat on the 48-year-old Italian.
Mancini defended his record on Friday and even suggested that defending their Premier League title was not beyond them.
"We started our project three years ago," he said.
"In three years we are always on the top - we fight for the title, we have won three trophies, we have the chance to win more this year.
"I always think we can do everything. We have 12 games, we need to do our best and not look at the table."
Leeds manager Neil Warnock, whose side knocked out Tottenham Hotspur in the previous round, said his side were relishing the thought of upsetting the English champions.
"We will give it a go on Sunday, and when you are underdogs, you do tend to come out of your corner fighting, because you don't want to be embarrassed," he said.
"It's just the quality of the opposition, though. Give them an inch, and they'll take a yard.
"We won't go there to shut up shop. We would lose for sure if we did that, so we may as well try and take them on and have a real go at it."
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