The only surprise, perhaps, was that Manchester City restricted themselves to six. The tie was so one-sided, the opposition so utterly abject, that there were moments when it was easy to imagine City would go even better than the seven they rattled past Norwich earlier in the season, never mind the six that Arsenal and Tottenham sieved inside this stadium. The fifth goal went in with more than a third of the game still to go and, after that, the goal machine that is Manuel Pellegrini's team must have been feeling charitable to add only one more.

Their latest haul, incorporating a stylish hat-trick from Alvaro Negredo, brings their tally to 59 goals in 15 home matches this season, keeping up the remarkable average of almost four every game. To put it another way, they have just won in straight sets – 6-0, 6-3, 6-0 – against three of London's top clubs. West Ham, once again, were shocking in their ineptitude, and Sam Allardyce's latest ordeal ended with the away fans making it very clear they did not want him as manager.

West Ham certainly did their bit to be remembered as the least distinguished team to visit this ground this season. It was a capitulation that makes the return leg a formality and means City can start their arrangements for a Wembley final against either Sunderland or Manchester United. Judging by the chants of "David Moyes is a football genius", their supporters do not seem too alarmed by the prospect of an all-Manchester affair.

West Ham, in stark contrast, move on to the game at Cardiff that Allardyce had always prioritised, lurching deeper into crisis and with it becoming increasingly clear that a good proportion of the club's followers have had enough. Allardyce was the subject of loud, abusive chants as he stood, almost motionless, by the touchline, his hood up in a filthy Mancunian downpour, hands firmly entrenched in his pockets. He looked a picture of misery.

At one point early on, Allardyce's team won a corner and the away end celebrated as though a goal had been scored. Unfortunately, in football it is never encouraging when supporters resort to gallows humour. The corner was cleared and it was the next piece of action that saw Yaya Touré pick out Negredo's run for the Spaniard to crack in a wonderful opening goal.

Negredo's perfectly judged volley came after 11 minutes and was probably the moment the West Ham supporters, who saw their team trounced 5-0 by Nottingham Forest in the FA Cup on Sunday, knew the night was about to become another public humiliation. Their team had Mohamed Diamé, a midfielder, playing in attack and a full-back, George McCartney, in the centre of defence alongside Roger Johnson, fast-tracked into the team after his loan from Wolverhampton Wanderers. They were out of their depth and afterwards it spoke volumes that Dzeko, scorer of the last two goals, talked about it being 5-0. The striker had evidently lost count.

Perhaps the most alarming part for West Ham was that their opponents were still a good notch or two below their optimum. The bottom line is that City did not have to be at their very best when the gulf was so considerable. Plenty of teams have taken a pummelling at City this season but not all of them have surrendered so meekly. For West Ham, it brought a now-familiar sense of embarrassment, with 11 goals conceded in four days.

Negredo's second was another beauty, flicking the ball into Dzeko, then running on to the return pass and sweeping a rising, diagonal shot beyond Adrián, West Ham's overworked goalkeeper.

The game was by now already an exercise in damage limitation for West Ham, and when Touré surged through the middle of their defence to make it three, six minutes before the interval, any lingering hopes of Allardyce's team finding a way back into the tie went from miniscule to non-existent. Those driving runs from Touré are a formidable sight, but there was something fairly wretched about the way Johnson simply retreated, backing away until Touré was in the penalty area and choosing where to put his shot. Johnson looked what he was: a Championship or League One defender trying to stop the most formidable attack in the land.

Negredo's hat-trick, taking him to 18 goals in 28 appearances, came early in the second half from another of those quick, penetrating moves through the opposition's defence, culminating in David Silva's pass and another classy finish from the striker's left boot. Dzeko made it 5-0 when he stabbed in Gaël Clichy's cross and the same player finished the rout with a handsome left-foot shot from the substitute Aleksandar Kolarov's cutback.

"We want our West Ham back," went the cry from the away enclosure.