Steven Gerrard's first-half strike from the penalty spot proved the difference as the hosts produced a performance far removed from their 3-0 league victory over the same opposition just last week.
The loss is City’s second at home in four days, following the defeat to local rivals Manchester United on Sunday, whereas the visitors found yet more cup success after their 5-1 win over Oldham last Friday.
With the absences of Kolo and Yaya Toure to consider, as well as Vincent Kompany’s four-game ban and David Silva’s late injury, Roberto Mancini was forced to make five changes to side that disposed of Liverpool last week. Stefan Savic, Mario Balotelli, Joleon Lescott, Nigel De Jong and Adam Johnson all came in to start the game.
There were just two changes from Kenny Dalglish, with Dirk Kuyt and Charlie Adam dropped from the side that started at the Etihad Stadium last Tuesday and replaced by Craig Bellamy and captain Gerrard.
Liverpool pressed from the off and Carroll was handed a fine chance for his side to open the scoring after the striker was set through on goal by Downing and shrugged off Savic to power a shot at the City net, but a commanding save from Joe Hart kept out the former Newcastle United man.
City had barely entered the Reds’ final third before Gerrard fired a stinging shot at Hart which dipped at the far corner, but the Blues’ ‘keeper reacted quick enough to palm the Liverpool skipper’s effort out for a corner.
From the set-piece, a rehearsed move between Gerrard and Downing had the latter testing Hart for the third time from distance. The winger’s wicked attempt on the volley from outside the box was deflected by a Liverpool attacker in the box, but the England international saw it just in time to instinctively push it out for another corner.
If that was an early let off for the hosts, they were to get no such sympathy moments later as Savic, who had an uncomfortable opening period, brought down Daniel Agger in the box to concede a penalty. Gerrard was subsequently handed his second chance to score from the penalty spot within a week, after his goal against Oldham, and he didn’t disappoint by sliding confidently past Hart.
City finally saw themselves test Pepe Reina with a shot on target from substitute Samir Nasri that came from distance and forced the Spaniard to get down and make the stop.
The hosts’ frustration though was left to simmer as no further conviction was showed by the men in blue and they appeared some way behind their visitors in terms of team spirit and convincing football, as both sides went into the break with Liverpool definitely the stronger outfit.
City woke up in the second half, but were helped by Liverpool’s intention to sit back and allow the Blues to attack them as they entered into a formation that saw six at the back. Sergio Aguero tried to punish the visitors with his dynamic running, but strong tackling and lacklustre final balls left the hosts frustrated.
However, Reina was the only ‘keeper in the opening 15 minutes of the second-half that was brought into action after Micah Richards leapt up for a corner and did well to get his head to the incoming ball, but the Reds’ stopper halted the effort well.
As the second period progressed Liverpool allowed City to continue to press upon them, a move that may have cost them their lead if it weren’t for tenacious tackling and failed attacks from the hosts. Aguero thus became something of a nuisance and took the Reds’ defence on numerous times but, unfortunately for the hosts, the Argentine couldn’t convert his skill into any serious effort on goal.Aguero went close once again near the end, his close range effort flying just inches over the bar, but City could not find the breakthrough meaning the Reds will be the much happier side going into the second-leg in a fortnight's time.
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