Here's how David Moyes's side rated at the London Stadium...
Alphonse Areola 6
Terrific save to deny Doucoure when the midfielder looked certain to put Everton two-up.
Vladimir Coufal 5
Fit after missing Olympiacos trip. Hardly worked defensively but no attacking product.
Kurt Zouma 5
Like his partner couldn't stop Calvert-Lewin on the turn for Everton goal. Beaten by same player in the air for Doucoure chance.
A few fine passes but fortunate to get away with mix-up with Paqueta. Rolled by Calvert-Lewin for Everton opener and increasingly second-best in their duel.
Aaron Cresswell 6
In for the suspended Emerson, set-piece delivery was decent.
James Ward-Prowse 5
Struggled with running power of Onana and Doucoure.
Edson Alvarez 4
With Soucek left out, handed extra responsibility in reshaped midfield but West Ham were too open. Poor in possession. Booked.
Jarrod Bowen 6
Missed big chance when scuffing wide midway through the first-half. Tried to inspire comeback with his drive but had precious few chances to run one-on-one as McNeil doubled up.
Mohammed Kudus 6
Handed a long-awaited first Premier League start. Deployed at No10, had a few bright moments but too often crowded out. Booked.
Lucas Paqueta 5
Divine pass almost made opener for Bowen but miscommunication with Aguerd should have been punished. Booked.
Strong start to the season has fallen away terribly. Cheers met his early withdrawal, which said plenty.
Said Benrahma (Antonio 57') 5
Booked for desperation to win ball back after losing possession. Volley forced Pickford into a decent save.
Tomas Soucek (Ward-Prowse 73') N/A
Danny Ings (Cresswell 85') N/A
Unused: Fabianski, Mavropanos, Ogbonna, Kehrer, Fornals, Cornet