City were rocked and boss Roberto Mancini brought on Adam Johnson for the last 20 minutes.
Instead, the gap remains at seven points, prompting some guarded optimism from City Manager Roberto Mancini.
Monday's late game saw a second straight win since he took charge for Manchester City manager Roberto Mancini.
Mourinho, who was recently hired to replace Roberto Mancini at Inter, coached Lampard for three seasons at Chelsea.
City's Roberto Mancini, meanwhile, has seemed likely to leave for months with his club reportedly courting Malaga's Manuel Pellegrini.
Inter coach Roberto Mancini has confirmed Hleb is one of the players the Italian club "would like to sign".
"A stupid, stupid, injury, " City manager Roberto Mancini had seethed the day before.
And even before Mourinho took charge, Inter had won three consecutive titles under Manchester City's current manager Roberto Mancini.
Trailing 1-0 from the first leg, Roberto Mancini's side conceded two first-half goals.
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"He can improve and be a great player for Manchester City for a long time, " said manager Roberto Mancini.
As well as the Italian giants, Roberto Mancini's team also face Salzburg of Austria and Lech Poznan of Poland.
The team has not denied a report that Malaga's Manuel Pellegrini has been approached to replace Roberto Mancini as manager.
He played in the 1986 and 1990 World Cups alongside players such as Roberto Mancini and the recently-retired Paolo Maldini.
The Londoners moved five points clear of Manchester City in fifth, though Roberto Mancini's side have a game in hand.
Inter Milan right-back Maicon is top of Manchester City manager Roberto Mancini's summer wish list, according to the Brazilian's agent.
Both Bellamy and Carlos Tevez were vocal critics of City manager Roberto Mancini's insistence on weekly double training sessions last season.
The man charged with turning City into a soccer juggernaut is Roberto Mancini, who replaced previous boss Mark Hughes in December.
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Santa Cruz figures in City manager Roberto Mancini's 25-man Premier League squad, despite much speculation that the Paraguayan striker would not.
Manchester City manager Roberto Mancini defended Houllier's decision to make eight changes.
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The striker's time at Manchester City was dominated by controversy, including an altercation with manager Roberto Mancini on the club's training ground.
Rather than thumping their chests, the two managers, City's Roberto Mancini and United's Sir Alex Ferguson, have spent this week playing down expectations.
Manchester City, without a manager after dispensing with Roberto Mancini, slumped to a 3-2 home defeat to Norwich, but had already clinched second spot.
He had an angry exchange with manager Roberto Mancini when substituted in the closing moments of his last match against Bolton on 4 December.
Both managers then made changes, with Ferguson sending on Nani for Darron Gibson and the Scot's counterpart Roberto Mancini replacing the subdued Adam Johnson with Patrick Vieira.
The 31-year-old has been linked with a six-month loan to his home-town club amid expectations that he will be left out of Roberto Mancini's 25-man squad.
Roberto Mancini's side were often excellent in their build-up play, however, they let themselves down with either the final ball or poor positioning of their forwards.
New rules mean each Premier League squad must now be capped, and the Wales captain feels he is not certain to be registered by manager Roberto Mancini.
City boss Roberto Mancini replaced Toure with Wayne Bridge before Tevez was forced off with a muscular injury, and the disruption it caused played into Arsenal's hands.
Roberto Mancini and Manchester City parted ways last week, which means that one of the best resourced, most desirable jobs in the game is now up for grabs.
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Rather than thumping their chests with confidence, the two managers City's Roberto Mancini and United's Sir Alex Ferguson have spent this week playing down expectations and talking up their opponents.
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