The Hammers were on course for a win when James Ward-Prowse’s 79th-minute penalty put them 2-1 up, after Ben Brereton Diaz’s debut goal for the hosts had cancelled out Maxwell Cornet’s opener.
But in the eighth minute of time added on, referee Michael Salisbury pointed to the spot after ruling Hammers goalkeeper Alphonse Areola had fouled Oli McBurnie and a further five minutes later, with the injured Areola replaced by Lukasz Fabianski, the Blades striker coolly converted.
Moyes did not directly criticise Salisbury, other than suggesting Areola was the player fouled, but said there is now a level of apathy towards the standard of referees.
“I am certainly not going to talk about any referees, for sure I don’t want to get myself into trouble,” he said.
“You should ask the referee and see what they think, we have got to the stage where we are settling for a level of officiating where we are all shrugging our shoulders and saying, ‘OK’.
“We are shrugging our shoulders again and seeing what they do. We don’t know what they are going to do.”
On whether Areola receiving lengthy treatment and having to be taken off meant he was the one fouled, Moyes added: “Absolutely, he was fouled. I think it was a foul on the goalkeeper.”
Moyes had just as much frustration with his own side, who were not at their best at Bramall Lane.
Cornet’s first Hammers goal at the 31st attempt put them ahead but Brereton Diaz levelled on the stroke of half-time.
Ward-Prowse’s penalty restored West Ham’s lead as the Blades’ Rhian Brewster and West Ham’s Vladimir Coufal were both sent off in added time for separate incidents before the real drama happened.
Blades boss Chris Wilder could not watch McBurnie slot the ball home but was pleased with his side’s staying power.
“I am delighted my team stayed in the game because with 10 men, and them passing it around, it could have gone from two to three,” he said.
“The attitude of the team has helped us stay in the game.
“The goalkeeper comes and makes a rash decision to come through and we get the penalty. I am delighted we got something from the game, that is my overriding emotion.
“I didn’t watch the penalty, I just saw the reaction of the crowd. It is just one of those – I do sometimes watch, not in the 103rd minute.”