After reaching the quarter-final stage of the competition last season, Slaven Bilic was hoping to reach the latter stages once again, but they came up against an impressive City team who will be match for any team in the tournament.
Yaya Toure fired City into the lead from the penalty spot, before Havard Nordtveit struck the ball past his own keeper to put the away side in pole position.
David Silva and Sergio Aguero scored either side of half-time before John Stones completed the rout late in the game.
The Hammers were looking to bounce back from the previous home defeat against Manchester United but they failed to reach the standards which saw them record a memorable double over the former Premier League champions last season.
City had early chances to break the deadlock after John Stones directed his header wide of the post and David Silva's close-range shot was kept out by the legs of Adrian.
Winston Reid produced a superb sliding challenge to deny Raheem Sterling getting on the scoresheet on 26 minutes.
Just seconds later Adrian then made a fantastic one handed save to tip a volley from Sergio Aguero over the bar.
City were rewarded for their early dominance when they opened the scoring on 31 minutes.
Angelo Ogbonna was adjudged to have brought down Zabaleta inside the box. Referee Michael Oliver had no hesitation in pointing to the spot despite strong protests from Ogbonna and his Hammers team-mates.
Toure stepped up and fired the spot-kick into the corner of the net.
It could have been a different story if the the Hammers had got back on level terms on 34 minutes.
Michail Antonio weaved his way into the box and saw his low shot superbly saved by City keeper Willy Caballero. The rebound fell to Feghouli but he dragged his shot wide of the goal.
City made the home side pay as they doubled their lead on 41 minutes. Bacary Sagna played in a dangerous cross from the right hand side and Nordtveit got in front of Sterling but turned the ball past his own keeper.
The game was put beyond the Hammers as Silva made it three on 43 minutes.
Sterling turned provider this time as he raced clear and crossed in for the unmarked Silva who had the easy task of striking the ball past Adrian.
City made it four on 49 minutes when Sterling cut the ball back for Toure who saw his shot turned home by Aguero.
The Hammers misery was compounded on 84 minutes when Nolito's corner picked out Stones and he headed the ball past Adrian.
Bilic will be hoping his players can get this defeat out of their system quickly and return to winning ways when they host Crystal Palace at London Stadium on Saturday 14 January.
West Ham: Adrian, Nordtveit, Reid, Ogbonna, Cresswell, Fernandes, Obiang, Feghouli, Lanzini (Noble 57), Antonio (Fletcher 71), Carroll (Payet 57)
Subs not used: Randolph, Calleri, Oxford, Quina
Bookings:
Manchester City: Caballero, Sagna, Stones, Otamendi, Clichy, Toure (Delph 77), Zabaleta, De Bruyne (Garcia 68), Silva (Nolito 57), Sterling, Aguero
Subs not used: Kolarov, Navas, Iheanacho, Bravo
Bookings:
Referee: Michael Oliver (Northumberland)
Attendance: 56,975