The FA Cup winners beat Stoke for the second time in four days, 3-0, to edge ahead of the Gunners in the race for an automatic spot in next season's Champions League group stage.
Now read Ian Ladyman's Eastlands match report: King Carlos the third
Farewell? Carlos Tevez (left) waves to the crowd after Manchester City's win over Stoke
Having lifted their first major trophy in 35 years, City can achieve their highest finish since 1977 by clinching third.
'That would be perfect,' Mancini said. 'For us it was important to get fourth when we started the season, but now we're in third. There's a big difference to fourth and having to qualify for the group stage.'
Getting shirty: Tevez celebrates his second goal (above) and fires Manchester City in front (below)
Tevez may not be at City to lead the European campaign after he said at the weekend he was considering leaving to be nearer his two young daughters in Argentina.
He responded to a standing ovation in the 88th minute last night by giving the crowd what appeared to be a farewell wave with both hands.
But Mancini said: 'I spoke with him many times in the last 20 days and it's my opinion that he will stay here next season. He said he wants to stay. He's got a five-year contract. We had a problem in December but everyone can change their opinion.
Phenomenal: Tevez scores his second goal against Stoke
'Carlos is an important player and a fantastic striker. I don't think he'd find at another club the feelings that everyone has for him here.'
If this was to be the City captain's final home appearance, he signed off in style by scoring the opening goal, then converting a 30-yard free-kick described by Stoke boss Tony Pulis as 'extroardinary'.
It put him level with Dimitar Berbatov as the Premier League's top scorer with 20 goals.
?Manchester City 3 Stoke 0: Tevez fires Mancini's men past Arsenal in race for EuropeWatch all the Premier League goals every week on our brilliant video playerPREMIER LEAGUE LIVE: Manchester City 3 Stoke 0 - the action from Eastlands as it happened35 and out! United haul down banner after City end long trophy droughtAll the latest Manchester City news, features and opinion
?Explore more:People: Carlos Tevez, Dimitar Berbatov, Tony Pulis, Roberto Mancini Places: Manchester, Argentina, Europe
Source: Daily Mail
Source: Daily Mail