A flood of bets was recorded across the country on Friday on Malaga boss Manuel Pellegrini taking over from the Italian at the Etihad, with the Chilean's agent recently spotted having lunch with City director of football Txiki Begiristain. Reports in Spain also claim a deal for Pellegrini to take over has already been agreed.
Pellegrini was backed at odds as short as 1/10 to become City manager and Mancini admitted the cut-throat world of football management meant he could not feel too settled.
"I won seven trophies at Inter in four years and they sacked me after four years," Mancini said. "This is football. I know football enough to understand this situation.
"I want to do only my job well, if it is possible, and continue to win every year. This is my target.
"I don't have other situations where I want to improve. I think it is important for every club to have a manager who can take a lot of decisions about the team, but now it is important we win this trophy."
Mancini went on to warn his side, odds-on favourites to lift the trophy at Wembley, that they should be taking nothing for granted against Roberto Martinez's Premier League strugglers.
"In England it is totally different because if you play against team who plays for relegation, if you want to win, you should play not 100, but 200 per cent," he said.
"For them it is the best moment in their life. If you don't play well, if you don't play a good game, you can't win.
"Every game we play against Wigan we have had a problem. We never win easy. First of all, they try to play football, always.
"Also, when they are losing a game, they continue to play football because they want to attack with a lot of players, and when they attack they are very dangerous.
"Never do they stay back too deep to defend the result. They don't play only counter-attack, they play football, they play to win."