The Argentina striker handed in a transfer request, which was immediately rejected by the club, a fortnight ago and once the issue became public, it dominated the agenda at Eastlands all last week.
But just hours before City's 2-1 defeat to Everton on Monday, which saw them miss the opportunity to top the table at Christmas for the first time in 81 years, the club announced that Tevez was staying.
Despite seeing his team's seven-game unbeaten run brought to an end, Mancini is hopeful that bringing to an end the Tevez distraction can only benefit his team, although he would not discuss the talks that took place with the player on Monday.
He said: "It's important news, the only good news this evening. It was very important for everyone, the squad the club, for him.
"It's important that we finish having to talk about this situation. We're happy for this.
"I think (the reasons for Tevez's U-turn) are not important. It's important that the situation was clear in this moment and everything went in a good way, that's important."
Mancini's team have earned a reputation for being rugged defensively but the Italian believes his team can only challenge for the title if they improve at the back.
He was angry with his side's defending against Everton and added: "We are frustrated because we had a big chance to go top after 18 games.
"It was a fantastic thing but now we must restart the season. We have to understand that we can't sleep when we play this game. then maybe we can go to the top in the future."
City fell behind at Eastlands when Tim Cahill scored his ninth goal of the season with an early header before Leighton Baines curled in a shot midway through the first half.
Everton's Victor Anichebe was sent off for two bookable offences but City could not make their dominance pay.
They pulled one goal back when Yaya Toure's shot deflected off Phil Jagielka and past Tim Howard but their challenge was finished when Kolo Toure was sent off in injury time.
Everton manager David Moyes saw his team climb to 14th in the table after they recorded a fourth Premier League victory of the season.
The Scot thinks his team have shown they have the potential to beat the best in the league but have to repeatedly perform against lesser sides.
Moyes, who lost Phil Jagielka to a thigh injury, said: "I said at the start that we can compete at the top end but we haven't been able to compete at the bottom end.
"We haven't been able to beat the teams below us, especially at Goodison Park.
"When it comes to the bigger games we seem to respond to the challenge and we're a match for a lot of teams.
"It's not just a victory because you're playing against a team who have the chance of being crowned champions at the end of the season, they've got a chance."
Moyes believes Cahill is in the best form of his career after the Australian midfielder's prolific finishing once again masked his strikers' deficiencies.
He added: "His energy levels looked back to the old days. There were signs that he'd maybe dipped down a little bit but he showed great energy and we needed him to.
"The work he had to do when we were at 10 men and even when we had 11, I thought he did a great job.
"Tim epitomised what we’re about, he was the one that kept taking the fight to Manchester City."