Sir Alex Ferguson can rarely have found a Liverpool home win so encouraging. Manchester City were taken apart at Anfield and that does not begin to cover their problems on a night when Roberto Mancini's promises of Champions League football and the FA Cup Final came with a smile but no substance.

The City manager accepted full responsibility for a calamitous warm-up for Saturday's FA Cup semi-final against Manchester United and vowed to learn from the lessons handed down by Kenny Dalglish's rampant team. He has plenty to occupy him. Carlos Tevez limped off early with a hamstring injury and, as has so often been the case this season, City's inspiration and guile went with him. His replacement, Mario Balotelli, was replaced due to his ineffectiveness, James Milner sulked when withdrawn and even the resilient rearguard that had conceded only 16 away league goals before this game was shattered as Andy Carroll scored the first two goals of his Liverpool career. His partnership with the irrepressible Luis Suárez eclipsed the visitors' own expensive attack in every respect and Dirk Kuyt converted, too, as Liverpool ended the contest inside 35 minutes.

City have now gone six Premier League away games without a win in 2011. They have not tasted victory outside Eastlands since Carroll scored for Newcastle United on Boxing Day and whether they will venture among the European elite next season is open to question with Tottenham three points behind with a game in hand and scenting a repeat of last year.

The two clubs' preparations could not have contrasted more greatly, with Liverpool bereft of defenders after defeat at Roy Hodgson's West Bromwich Albion and City having rested players from their rout of Sunderland. Yet the difference in their responses was even more profound. Liverpool were outstanding, City woeful. The home side compensated for absentees with spirit, ingenuity and individual excellence; the visitors were laboured, lethargic and devoid of imagination. On this evidence Sheikh Mansour's investment policy should focus more on talent and attitude rather than simply height.

A collective effort earned its standing ovation from the Anfield majority but no one epitomised Liverpool's superior level of performance and desire better than the debutant John Flanagan. The 18-year-old had not made even a substitute's appearance before being drafted into a depleted defence at right-back yet settled superbly. Liverpool's initial reluctance to give Flanagan the ball proved unnecessarily protective. A sweeping cross-field pass to Fábio Aurélio would have soothed any nerves in the teenager and defensively he was faultless, crunching hard but fair into Gareth Barry and muscling aside Balotelli as the Italian tried to break through on goal.

Balotelli's presence – and pitiful contribution – was indicative of City's evening. In the 13th minute Tevez was dispossessed by Carroll and pulled up in the process. He was quickly withdrawn but not before his opponent had swept Liverpool into the lead with an unstoppable drive beyond Joe Hart. Carroll's tackle on Tevez allowed Raul Meireles to strike from distance, though only into Vincent Kompany, and the rebound was returned with interest by the England striker as his low, left-foot drive beat Hart purely for pace and power, not precision, and Anfield erupted to acclaim Carroll's first goal since his £35m transfer from Newcastle.

Hart had previously tipped a Suárez shot on to the post when the Uruguayan, displaying a sublime touch and an unerring knack of finding space all over the pitch, was sent through by Carroll's quick thinking. The England goalkeeper was beaten when Meireles, Suárez and Aurélio had shots blocked inside the area. The latter's effort was deflected across the area by Kompany, who appeared a lone defender against the Liverpool tide, and Kuyt picked his spot into the far corner.

City were reeling, in complete disarray and seconds later Carroll glanced his second of the night past a despairing Hart when he towered above Aleksandar Kolarov to meet Meireles' cross with a glancing header.

In contrast to the pedestrian Edin Dzeko and Balotelli, Carroll and Suárez looked a double-act of rich potential. They embarrassed their City counter-parts in terms of industry and threat. City's £25m Italian substitute suffered the ignominy of being withdrawn with seven minutes remaining and, even with Tevez injured, his manager refused to offer the excuse that his withdrawal was a protective measure. He is the kind of signing that gets a manager the sack. Liverpool saw out the game comfortably. City can look towards Wembley with trepidation.