Yaya Toure's late curling strike clinched a 2-1 win for City over West Ham.
City were heading for defeat until Yaya Toure equalized with a deflected long-range shot.
Goals in either half from Sergio Aguero and Yaya Toure earned Manchester City a 2-1 against West Ham United at the Etihad Stadium.
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When Foster plucked a Yaya Toure shot out of the top corner, their deserved point was secure, while Mancini's future became less so.
City, who won the match 2-1 at the Estadio do Dragao, complained after Yaya Toure and Mario Balotelli were the target of racist chants.
Everton lost Victor Anichebe to a second booking on the hour and City pulled a goal back when Yaya Toure's shot deflected in off Phil Jagielka.
He is eager to start work and plans to head to Europe to watch the likes of Didier Drogba, Emmanuel Eboue, Salomon Kalou, Kolo and Yaya Toure.
But the match will also be remembered for a terrible miss from Tevez, who spooned an open goal over from 12 yards after being set up by Yaya Toure.
Villa were 1-0 down after only five minutes when Yaya Toure lashed the ball home and Houllier was adamant that not even his regular XI could have prevented the strike.
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The home supporters' unbridled joy at what would have proven a tie-winning goal was short-lived, though, as the referee had given a handball against Yaya Toure in the build-up long before.
City dominated the first 20 minutes as Yaya Toure's surging runs repeatedly caused problems for Chelsea, although Aguero and Carlos Tevez both failed to test Petr Cech with shots from tight angles.
Milner - the current Professional Footballers' Association young player of the year - joins Yaya Toure, David Silva, Jerome Boateng, Aleksandar Kolarov and Mario Balotelli in moving to Eastlands this summer.
Yaya Toure's first-half goal appeared to set City on course for a win that would have virtually guaranteed a place in the top four as they exerted total domination over the Toffees.
Striker Emmanuel Adebayor and defender Vincent Kompany were seen arguing during Saturday's defeat, while Yaya Toure and Milner were understood to have had a disagreement at the interval during the defeat by Arsenal.
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However, he did come on as a replacement in the second half for his 92nd international appearance as Yaya Toure and another substitute, Didier Ya Konan, scored late goals to add to Gervinho's first-half opener.
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Boyata's dismissal saw Yaya Toure drop into defence but City were still enjoying the lion's share of possession and their formation - switching fluidly between 4-4-1, 4-2-2-1 and 4-2-3 - caused Arsenal plenty of problems.
City created another gilt-edged chance to break the deadlock on the stroke of half-time when James Milner's free-kick found its way to the unmarked Yaya Toure six yards out - but Mignolet managed to divert the Ivorian's effort narrowly wide.
Right-back Daniel Alves returns from his domestic ban and midfielder Yaya Toure could play despite suffering an injury against Bilbao, while reserve players Andreu Fontas and Jonathan dos Santos were included in the squad, Barcelona's Web site reported on Monday.
Sunderland's defence was caught wide open as Yaya Toure showed superb pace and strength to power 50 yards through the midfield before laying the ball off to Tevez but the striker - under no pressure - incredibly side-footed his effort well over the bar with the goal at his mercy.
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