West Ham boss Moyes, the former Manchester United manager, was furious to see Arthur Masuaku penalised at the end of the first half for a foul on Salah and even more frustrated with the officials for not overturning the decision.
Pablo Fornals had opened the scoring for West Ham after just 10 minutes before Salah was brought down in the area by Masuaku.
The Egyptian winger made no mistake slotting home to level the scores at half-time.
And while Sadio Mane had a second-half goal disallowed, super sub Diogo Jota came off the bench to hand Liverpool a win and send them to the top of the table.
The result frustrated Moyes, whose side sit 13th in the Premier League, and he accused Salah of cheating to con the referee with a dive.
‘It’s not the sort of football I want to be involved in,’ raged Moyes.
‘I think our player stops and throws his arms up because he’s so disappointed about the dive. I’m just disappointed they didn’t turn the decision around.
‘Maybe in the second half a decision went for us, but the first-half one didn’t.
‘I am amazed the penalty kick was given for the action in the first half. I really am. I am getting disappointed now.
‘We are disappointed. I would not say we were unlucky.
‘One of them went for us as they had a goal disallowed but at 1-0, the penalty was given.’