Manager David Moyes admitted West Ham had to ride their luck to get a battling point at Stamford Bridge.
Chelsea had 22 attempts on goal, while West Ham managed just four – only two of which were on target.
But the Blues paid the price for numerous missed chances and Hammers substitute Javier Hernandez earned a point with a fine strike three minutes after coming on.
“I was thrilled to get in at half-time just a goal down,” Moyes said.
“We gave away a poxy goal but at 1-0 you are always in it.
“Whoever plays Chelsea will need a good goalkeeper. They were terrific at times. Their combination play, with Morata, Hazard and Willian, would have made it difficult for any team.”
Moyes also paid tribute to Hernandez and England international goalkeeper Joe Hart.
“Javier is a great penalty-box striker,” Moyes said. “If you wanted the chance to fall to someone in the box then he is as good as anyone.
“Joe showed why he has got so many caps, so many medals and has played at the top level.”