The main talking point was Gareth Barry's challenge on Kevin Nolan in the first half, when the Hammers captain looked like he would have a clear run into the penalty area which match official Jon Moss saw as fair.
"I don't think there is much in there. There is a bit of contact but Leighton Baines is recovering and I don't think that is an incident the referee can give as a free-kick," said Toffees boss Roberto Martinez.
"I think you are looking for those actions too much. I think the referee did the right thing to play on.
"When I watched it live, I didn't feel it was a free-kick."
Hammers boss Sam Allardyce, understandably, felt differently.
"There's no doubt about that in my mind," he said.
"Kevin would have been perhaps scoring another goal because of the goalscoring form he is in; he's scored four in the last five.
"It looks like he (Barry) is stopping a goalscoring opportunity and a red card. I am really disappointed in that but I can't control that."
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