The defeat means that Chelsea's slim hopes of retaining the title are all but over and Twitter was not happy with this.
Antonio Conte said on Saturday that Chelsea's title defence was all but over after four defeats in the opening 16 games of the season and added that, in his opinion, it had never even got off the ground. I saw the same game [with West Ham] against Manchester City, where Manchester City attacked for the whole game against the whole team behind the ball. "Because we have got a couple of cup games, we have got an incredibly busy period".
Chelsea defender, Gary Cahill says the blues were way off their best form, following their 1-0 loss to West Ham.
"To talk about the title race after a defeat I think is a bit odd", he said.
'Many players were exhausted today. When you have this task it is impossible to think that you are in the title race. It's normal when you play every three days.
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"My experience is this, that if you want to stay in the race for the title, in the first part of the season you can lose once, twice [and no more]. We allowed them to get the early goal which was a poor goal to concede on our behalf because we've been tight at the back of late", the Blues captain told Sky Sports.
"It's frustrating in terms of wasting a bit of time, which was clever play from them, but we weren't at the races today for whatever reason". Instead we created the chances but didn't take them.
Marko Arnautovic's early strike was backed up by a resilient defensive display that ended an eight-game winless run for the hosts and provided a first victory under David Moyes. Now we are talking about a defeat. I repeat, we create many chances but were not able to score.
'We will try to do our best this season but if you remember I said it would be very, very tough.