"Roberto's going to do a wonderful job for us for many years," Mubarak said in a video interview on the City website.
"Roberto is our manager. He's done an excellent job coming in mid-season, organising the team. I'm very happy, and (owner) Sheikh Mansour is delighted with the way he's organised the team."
City's chance of fourth place in the Premier League and a berth in the Champions League disappeared with Wednesday's 1-0 home defeat by Tottenham Hotspur.
That led to media speculation that Italian Mancini could be fired. He arrived in mid-season to replace Mark Hughes who had also been given public assurances about the owner's long-term faith in him.
"We believe he is definitely the right manager for this club for many years. What he needs this summer is time to prepare and really organise ourselves," Mubarak said.
"We know the areas that need to be improved within the club. A good pre-season followed with a good start to the season and I'm really excited for next year.
"It's been a wonderful season. We've gone a long way as a team and I feel very good about next year because we've crossed an important milestone as a club. Next year's going to be a very important year for us.
"It's been an incredible season. We can focus on last night or we can focus on the season as a whole - I prefer to do that.
"Fifth is not where we would like but it's a major jump. It's a major achievement for this club to move from 10th to fifth place."
