Mancini has praised his side's character and insists that City registered a crucial victory.
"I hope it's the last day like this. It's important we won this game, because the first day is always difficult," Mancini told Sky Sports News.
"It is important we have character. We understand that we have to close the game before because we had many chances to close out the game and we didn't do it.
"It is normal for us. It happened last year two or three times, but I think today it was only because it was the first game. We've only been back for two weeks."
Next up for City is a trip to face Liverpool on Sunday.