"We get a point, that is the important thing".
Chelsea began to crank up the pressure shortly after, increasingly filtering their play through Hazard and Willian.
Conte had admitted losing at home to Tottenham for the first time in 28 years last weekend was a huge setback in Chelsea's bid to salvage a dismal campaign by qualifying for the Champions League.
It was a "crazy day" for Declan Rice at Stamford Bridge.
Hazard was looking more like his old self and he combined with Cesc Fabregas to prise open the West Ham defence, but Morata's deft back-flick rolled wide.
Within five minutes the hosts were ahead.
Victor Moses' cross bounced around the West Ham area before falling to the feet of Azpilicueta, who could not miss from a couple of yards out. Chelsea kept up the pressure but couldn't grab a second before the interval. They were terrific at times. The Spaniard's performance forced West Ham to defend for most of the game.
But Chelsea remained firmly on top.
Chelsea's swagger initially continued after the interval, with Willian dragging a shot just wide and Morata heading over from a corner.
They would come to seriously regret not adding a second.
Just a few minutes later, his global team-mate did what he had failed to do.
Suddenly momentum was with the visitors.
And he feels that West Ham were well backed by their supporters in a game which the Hammers knew could play a big part in securing Premier League safety. Finally it felt like a fierce London derby as the goalmouth action came thick and fast.
Hernandez's goal was therefore crucial.
Antonio Conte slammed his misfiring Chelsea stars as their hopes of a top-four finish in the Premier League suffered a potentially fatal blow in a 1-1 draw against West Ham on Sunday. It was end-to-end stuff at this stage and it looked as though N'Golo Kante had executed a brilliant last-ditch tackle to thwart Arnautovic when he was bearing down on goal but after seeing replays, the Frenchman went through the man to play the ball. Hart, who will be itching to get himself in England's World Cup squad, got down brilliantly to get a finger-tip on Giroud's header, pushing it onto the post and out for a corner.