During that run, they have crashed out of the Champions League at the last-16 stage, beaten over two legs by a much-fancied Barcelona side, but FA Cup glory could be a potential silver lining in an otherwise disappointing season, as the Blues are into the last four of that competition.
Chelsea took a deserved lead through Cesar Azpilicueta on 36 minutes and mustered 23 efforts on the West Ham goal, but a combination of poor finishing and inspired goalkeeping from Joe Hart ensured the game was still close when Hernandez replaced Gelson Fernandes with 20 minutes remaining.
And this morning they lie a dismal 10 points off the top four and Champions League football, with six games left.
West Ham were nearly pegged back again on 79 minutes as Marcos Alonso fired a long range effort but Joe Hart produced a brilliant save to deny the Spanish defender.
Wilkins, who began an impressive playing career at Stamford Bridge and also later coached them, died on Wednesday aged 61 following a cardiac arrest. When you stay in this position in the table it means that you have a problem. Edmilson offers far more than Hernandez in the middle of the pitch, but the Mexican provides obvious goal threat - and he only needed one chance, sweeping the ball home right-footed with typical composure to level the proceedings. This game is our season, it is a pity because we dominated the game and created many chances to score.
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The Italian was answering Gianluca Vialli, who recently said that Conte "couldn't wait" to leave West London. To speak about the gap between us and Manchester City now is not right.
Conte was at a loss to explain how his side failed to take all three points, but did seem to question his players' desire to capitalise on their complete control. A good performance, yes, but many times we have had a good performance and lost the game, or drew the game, many times we've had a good performance but not won the game.
"We must win this game".
"We are very sad because it is very hard to accept this news". Willian shot wide, Moses blazed over and then drilled wide. "We must be realistic to understand the reality", he told reporters ahead of the West Ham match.