Peter Crouch's goal eight minutes from time at Eastlands ensures the London side will secure fourth spot at least in the Premier League. City can finish fifth at best.
Italian Mancini was appointed in December, with City chief executive Garry Cook admitting he was concerned that Mark Hughes would not bring Champions League football to the wealthy club.
Asked if he was confident he will still be at Eastlands next season, he said: "Yes, why not?
"I think that I will stay here and why not? I've worked for five months and next season we will build a team and we can have something special.
"We are disappointed because we had the chances but at the same time we must be proud because we did a good season and we're not playing Champions League football next year but we will try in the Europa League.
"If we'd got fourth, we did a good job. When you miss fourth by one point or two points, we did a good job.
"I work because I want to win. Now we have a good team and we can improve next year."
He said: "It's a good achievement and it's nice. I'm just pleased the players have done great.
"It's better than winning the cup with Portsmouth because it's over a whole season.
"We will have a go in the Champions League. What can you do but have a go?"
