A victory in East London would have seen them open up a six-point gap to the point three, but the defeat now sees the Hammers draw level.
Burnley now face a difficult challenge against third-placed Chelsea, who comfortably beat bottom side Wolves 3-0 in their last encounter.
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In previous games against the league’s biggest and best teams, Parker has opted to switch to a back five in a bid to frustrate their opponents – but despite being competitive in the majority of these games, they’re yet to pick up any points.
Does the Clarets boss stick with the same approach? Or keep faith with the back four?
Here’s how we expect Burnley to line up:
Hopefully his confidence won't be too dented by his two mistakes against West Ham and Slovakia's 6-0 thrashing by Germany (Photo by Alex Livesey/Getty Images)
1. GK - Martin Dubravka
Hopefully his confidence won't be too dented by his two mistakes against West Ham and Slovakia's 6-0 thrashing by Germany (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey
Walker's pace and power will be key to stop Chelsea getting in behind (Photo by Justin Setterfield/Getty Images)
2. RB - Kyle Walker
Walker's pace and power will be key to stop Chelsea getting in behind (Photo by Justin Setterfield/Getty Images) Photo: Justin Setterfield
Despite his penalty miss, Tuanzebe should be full of confidence after helping DR Congo reach the inter-confederation play-offs (Photo by Richard Pelham/Getty Images)
3. CB - Axel Tuanzebe
Despite his penalty miss, Tuanzebe should be full of confidence after helping DR Congo reach the inter-confederation play-offs (Photo by Richard Pelham/Getty Images) Photo: Richard Pelham
The Frenchman looks a lot more settled playing in a back four than he does in the back five (Photo by Richard Pelham/Getty Images)
4. CB - Maxime Esteve
The Frenchman looks a lot more settled playing in a back four than he does in the back five (Photo by Richard Pelham/Getty Images) Photo: Richard Pelham