Having beaten the likes of Chelsea and Liverpool in recent weeks to justify their place in the top four, the Hammers found Burnley more stubborn opposition as Nick Pope thwarted the handful of clear openings they were able to carve out at Turf Moor.
But things might have been different had Graham Scott pointed to the spot when Craig Dawson went down after a tangle with Dwight McNeil in the penalty area late in the first half.
VAR Jon Moss upheld Scott’s decision after the two players appeared to collide when chasing a loose ball following a corner.
But though Moyes was hardly clamouring for a penalty himself, given some of the soft decisions which went the way of Manchester City, Chelsea, Liverpool and Manchester United this weekend, he questioned what the standard now was.
“I think this weekend we have seen more soft penalty kicks given in the Premier League than all season so I think if those ones were given, I would expect today’s to be given,” he said.
“But I am an advocate of it has got to be really correct. I think today’s was worthy of that, if that is the level of penalty kicks…
“I have really enjoyed the refereeing this year. I think it has been excellent. I think VAR has done as well as it can do but after watching the penalty kicks yesterday, what would the difference be?
“If yesterday they got it wrong, it would be great if they came out and said that. Today’s one was, I thought, poorer than the ones yesterday.”
The draw leaves West Ham only one point clear of fifth-placed Manchester United, with Arsenal and Tottenham also within touching distance.
Following the high of last weekend’s last-gasp 3-2 win over Chelsea, this was a case of two points dropped in the pursuit of Champions League football.
“It is part of growing your club,” Moyes said of the setback. “We have said we would like to challenge the top teams. Last season we had a near-perfect record against the teams below us. In this period we have not quite done as well as we could have done.
“It is just a little bit hard to get to that point and get a little bit extra.”
On the rare occasion West Ham did carve out a clear chance, Nick Pope was in the way. In front of the watching Gareth Southgate, the seven-times capped England goalkeeper made close-range saves from Issa Diop and Said Benrahma in either half, then denied Jarred Bowen late on.
“The top level keeper that he is, he will be pleased he has made the saves but they are ones you would fancy him to make,” Burnley boss Sean Dyche said. “The defensive unit was strong again…
“I thought it was a good game for (Pope), a solid game. I don’t think he will be thinking about Gareth Southgate being here, Gareth has been here a number of times.”
For Burnley it was definitely a sense of one point gained, even as they continue to languish in the bottom three having won only one game all season.
“We will take a point,” Dyche added. “We weren’t near the mark in the first half, we looked a bit nervous and anxious. We didn’t find any flow to the play, that can happen and there was a nervousness…
“In the second half we were a lot better, not enough to win the game but a lot better…I think it is a point gained in the sense that they are a good outfit.”