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West Ham manager Slaven Bilic said he 'feels for' Chelsea manager Jose Mourinho - but the incidents in the game were not mistakes but "matters of opinion".
Mourinho was sent to the stands at half-time after apparently trying to enter referee Jonathan Moss' dressing room at half-time.
Nemanja Matic had been sent off for two yellow cards and Cesc Fabregas was ruled offside when he seemed to be on - his goal was disallowed.
The Portuguese manager refused to speak to the media after the match and will likely face action from the Football Association.
Hammers manager Slaven Bilic said he had not spoken to Mourinho since the final whistle.
"I feel for him," the Croatian said. "Decisions from his point of view have gone against him. I would moan if it was against us. But they are not mistakes - they are matters of opinion.
"The sending-off I didn't see. The first one was definitely yellow, the second one was very far from me, but it looked like Sakho was already gone.
"But I think second yellows, especially in the first half, should be 'proper' bookings. The disallowed goal? No-one can say onside or offside even when you freeze the picture."
Show all 23 1 /23West Ham vs Chelsea - player ratings West Ham vs Chelsea - player ratings <b>West Ham:</b> Adrian - 7 out of 10 Made a one-handed acrobatic save to deny Fabregas’ corner early on before superbly saving Willian’s free-kick later. He then combined with Lanzini to clear Zouma’s header off the line but couldn’t do much to keep out Cahill’s powerful equaliser.
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West Ham vs Chelsea - player ratings Carl Jenkinson - 6 out of 10 Performed well against the threat of Hazard, but was outmuscled enough by Zouma to put him off clearing the ball in the build-up to Cahill’s goal.
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West Ham vs Chelsea - player ratings James Tomkins - 7 out of 10 Former a solid partnership with Collins to keep Cost quiet all game.
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West Ham vs Chelsea - player ratings James Collins - 7 out of 10 Made several key clearances to deal with Chelsea’s attacks while
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West Ham vs Chelsea - player ratings Aaron Cresswell - 7 out of 10 Performed well to keep a grip on Willian in the game, although there were moments he was outrun by the Brazilian. However, he played the key ball into the area that Carroll secured the win from and he will see this as a fine game.
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West Ham vs Chelsea - player ratings Mark Noble - 6 out of 10 Performed well to marshal his side and deal with danger in the middle of the park.
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West Ham vs Chelsea - player ratings Cheikhou Kouyate - 6 out of 10 Worked well in midfield to contain Fabregas in the first half, but allowed Cahill to run free before he equalised. Still, it didn’t matter too much with Carroll later scoring.
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West Ham vs Chelsea - player ratings Manuel Lanzini - 7 out of 10 Despite playing through the middle, the winger kept dropping to the flanks to cause Chelsea all sorts of problems. But he carried out his defensive duties well ded – bullying Fabregas off the ball in one incident before clearing ball from Costa’s path and cleared Zouma’s header off line. Should have made it 2-0 but chipped ball over bar with time and space.
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West Ham vs Chelsea - player ratings Dmitri Payet - 7 out of 10 The winger won and took the corner that Zarate scored from while creating several other chances for the home side. His pace caused Zouma problems especially as he regularly linked up with Lanzini to create attacks.
West Ham vs Chelsea - player ratings Mauro Zarate - 8 out of 10 Scored West Ham’s opener in the 15th minute with his low drive after finding himself completely unmarked. Had less of an impact going forwards than Lanzini and Payet, but stepped up when needed.
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West Ham vs Chelsea - player ratings Diafra Sakho - 5 out of 10 Endured a very quiet game and did not make an impact up front for the home side.
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West Ham vs Chelsea - player ratings From the bench: Andy Carroll - 8 out of 10 Was brought on for goalscorer Zarate and the striker outmuscled Cahill to make it 2-1. An inspired substitution.
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West Ham vs Chelsea - player ratings CHELSEA: Asmir Begovic - 6 out of 10 Did well when forced into action but again, was let down by his defence.
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West Ham vs Chelsea - player ratings Kurt Zouma - 6 out of 10 The defender’s header came to within an inch of giving Chelsea the equaliser, but goal-line technology ruled it just on the line. The Frenchman played a part in the Blues’ equaliser, applying the pressure to put Jenkinson off clearing Willian’s corner, which eventually fell to Cahill. However, he did have a few moments where he appeared unsure in his new position of right-back.
West Ham vs Chelsea - player ratings Gary Cahill - 6 out of 10 Got Chelsea back into the game when he equalised with a fine shot in the 56th minute – his first Premier League goal in 350 days – but was outjumped by Carroll for West Ham’s second goal.
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West Ham vs Chelsea - player ratings John Terry - 5 out of 10 Initially defended well, but was to blame for failing to adequately clear the ball in the build-up to Carroll’s match-winning goal.
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West Ham vs Chelsea - player ratings Cesar Azpilicueta - 5 out of 10 Left Zarate complete unmarked for the opener before being shown a yellow for a foul on Lanzini. In contrast to recent weeks, looked more vulnerable at left-back against the Hammers.
West Ham vs Chelsea - player ratings Ramires - 5 out of 10 Struggled to contain the pace and trickery of Lanzini, Payet and Zarate ,who kept interchanging and running riot in midfield. Was brought off for Falcao in the dying stages of the game.
West Ham vs Chelsea - player ratings Nemanja Matic - 3 out of 10 After failing to control Lanzini in the middle of the park, the midfielder needlessly got himself sent off in the 44th minute after pulling back Kouyate before fouling Sakho.
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West Ham vs Chelsea - player ratings Cesc Fabregas - 5 out of 10 His chipped ball created a good chance for Costa early on, but the midfielder once again failed to impress and it was his foot, which the ball deflected off in the build-up to West Ham’s opener before his goal was flagged as offside. Was hauled off at half-time for Mikel.
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West Ham vs Chelsea - player ratings Willian - 6 out of 10 Worked hard, as usual, for the Blues on the left flank but did not create any clear-cut chances. Was one of Chelsea’s better players on the day.
West Ham vs Chelsea - player ratings Eden Hazard - 5 out of 10 Was hardly involved in Chelsea’s attacking play in the first period as Jenkinson shackled him well and didn’t do enough with his one good chance in the second period.
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West Ham vs Chelsea - player ratings Diego Costa - 5 out of 10 Should have done better with the two shots he had in the first half but fired one high and the other wide. Was kept quiet by Tomkins and Collins all afternoon and spent the game largely as a bystander.
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The furore surrounding Mourinho took some of the spotlight away from West Ham, who added Chelsea to Arsenal, Liverpool and Manchester City in their list of high-profile scalps this term.
Bilic added: "I'm very proud of my team and my club. It's brilliant to win against the champions at home."
Additional reporting from PA
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