Andy Carroll's first goals since his £35m move to Liverpool put a dent in Manchester City's Champions League hopes as they were emphatically swept aside at Anfield. Carroll struck twice - the first a spectacular long-range strike - as Liverpool established a deserved three-goal lead by the interval and kept their own European ambitions alive with a vibrant display. Dirk Kuyt sandwiched a goal in between Carroll's double as City endured a night of total misery, with captain Carlos Tevez limping off early on with a hamstring strain that puts a serious question mark over his participation in Saturday's FA Cup semi-final against Manchester United at Wembley. Mario Balotelli replaced Tevez but his contribution was so negligible that he suffered the indignity of being substituted himself as time ran out, a development that encapsulated a wretched 90 minutes for City and boss Roberto Mancini. Carroll has been edging slowly towards full fitness after his expensive arrival from Newcastle United and his partnership with £23m Luis Suarez showed rich promise as Liverpool controlled affairs from start to finish. Mancini's side remain in fourth place but an opportunity to press home an advantage over closest rivals Tottenham was squandered with a lamentable display. Liverpool's performance - despite a defensive injury crisis that saw a promising debut for teenage academy graduate John Flanagan - was a resounding advert for Kenny Dalglish to be given the manager's job on a permanent basis. And The Kop made their feelings clear on the matter throughout as they sang their support for the Anfield icon, who they want to take Liverpool on to the next stage of their recovery from the ill-fated Roy Hodgson era. City, in contrast, were listless and portrayed all the signs of a side with their sights on the meeting with archrivals United at Wembley - mystifying giving the stakes still on offer in the Premier League. The difference between the sides was illustrated by the threat posed by the opposing strike partnerships. Carroll and Suarez were danger personified while Edin Dzeko and Balotelli never laid a glove on Liverpool's defence. Mancini must now marshall his forces before Saturday, with the bitterest blow of all from a night of despair being the injury to talisman Tevez, the inspiration behind much of their progress this season. City kept David Silva and Nigel de Jong on the bench ahead of Saturday's Wembley date - and the pair may well have been relieved to have kept their distance from the wreckage of that first-half display. Liverpool were seriously weakened by injuries, with captain Steven Gerrard and Daniel Agger out for the season and Glen Johnson also missing, but it did not stop them running riot against laboured City. The dangerous Suarez delivered an early sign of the carnage to come when he outstripped City's defence but keeper Joe Hart got a faint and vital touch to turn his shot on to the post. City were barely hanging on as Liverpool's pace and movement proved too much and the breakthrough came in spectacular fashion after 13 minutes. Carroll was lurking 25 yards out and when Vincent Kompany deflected the ball into his path he thrashed a low left-foot finish past the startled Hart. And moments later matters took a desperate turn for the worse for City when Tevez pulled away from a challenge with Carroll, the Argentine clutching his hamstring, removing his captain's armband instantly before disappearing disconsolately down the tunnel. The enigmatic Balotelli entered the fray but he was little more than a bystander as Liverpool emphasised their superiority by adding two more goals inside a minute as City collapsed. Kuyt scored the second 11 minutes before the interval with a perfect side-foot finish past Hart, then Carroll rose with Aleksdander Kolarov to glance in Raul Meireles' angled delivery. The second half was little more than a procession as Liverpool closed out victory, although City's black mood was reflected in the unhappy reaction of James Milner when he was substituted for Silva. Liverpool were the side looking more likely to add another goal and Hart needed to be alert to plunge low to save from Meireles as he drove in a low shot from 12 yards. Liverpool goalkeeper Pepe Reina was effectively unemployed until the 82nd minute when he punched away a powerful drive from Yaya Toure. Balotelli's lifeless effort, although in his defence he was hardly alone and certainly no worse than the bitterly disappointing Dzeko, came to a conclusion when he was replaced by Nigel de Jong. The pattern had long since been set though and Carroll only just missed out on a hat-trick when his header dropped on to the top of the net with Hart scrambling. Source: BBC