West Ham boss David Moyes said: "It is a game where we missed the opportunity. We had an opportunity to challenge the teams above us but we have missed it.
"It was a terrible injury to Ashley Westwood, which derailed the speed of the game for a while. We lost concentration during that period, but that was our fault and nobody else's.
"We were playing quite well and knocking on the door at that time but went on to concede the goal. We had a great chance to win the game with the amount of chances and we probably should have.
"We have been doing OK up until now. We will keep ploughing on and keep picking up results. He [Nick Pope] had a couple of really good saves but hopefully we will score them in the next games."
Burnley interim boss Mike Jackson said: "It wasn't nice to see and it had an effect on the lads. He [Ashley Westwood] has been taken to hospital and hopefully it is not as bad as expected, but best wishes go to him. Straight away, you just knew. We just hope it is not too bad.
"With what has happened in the past week, and today with Ash [Westwood], we could have got the three points but it's a good point for us on the road. It is something to build on."
On Nick Pope's performance: "That is why he is in that England group. They are terrific saves but they are the standards he sets himself.
"In a strange way, I did enjoy it, it has been manic. That is where I'm happiest on the grass. It is where I'm most comfortable."