Liverpool's players failed to recover from a first half where they were bullied by United and failed to deal with the hosts' direct and aggressive approach.
A third successive Premier League defeat saw West Ham slip closer to the relegation zone and Moyes accepts his side are going through a hard spell.
Icelandic winger Gudmundsson has been one of the stand-out Burnley players this season, scoring twice and setting up six goals as well as many more chances with his excellent delivery from the left.
West Ham United head into Saturday's clash with Burnley with veteran defender Pablo Zabaleta hailing the showdown the first of "nine finals" as the Hammers continue their desperate fight against relegation.More news: The Grand Slam is on as Ireland defeat Scotland in exciting showdown
Despite a couple of delays, the match was played to a finish and afterwards Hammers manager David Moyes told Sky Sports: "We want the supporters behind us, but you can't cross the line and come onto the pitch".
"I've said it all along, Joe's been good, and I've got competition in some places, so you have to play well".
While the official investigation of the incidents will be carried out by the FA, ...
"Actually the big thing was to say get on with it - keep playing".
"There's going to be more pressure on them than there is on most of those teams at the bottom because there's newly promoted teams and there's teams that aren't seen as (being) as good as West Ham". If we go, that is. "I'm confident we have the players here". At the prices I think it's worth backinng Palace to come away with a point at least. While Burnley had started the game well, Everton took the lead after 20 minutes with Jordan Pickford performing heroics in the Toffees goal to prevent the Clarets coming back into the match. With Wood and Barnes proving too much for Everton to handle, they grabbed a goal each to fire their team ahead and to a deserved three points. With Burnley's iron curtain of a back four - only Man City have conceded more on the road - and West Ham's struggling strike-force, I think this could end all square, and the [3.25] makes plenty of appeal.