Pablo Fornals had put Moyes' side ahead after just 10 minutes at Anfield but the Reds were handed a way back into the game after Arthur Masuaku was ruled to have fouled Mohamed Salah in the box just before half-time.
Replays showed the defender did fail to make contact with the ball and clipped Salah – who went down in a clear attempt to win the spot-kick before calmly converting the penalty.
Moyes was less than impressed to see the penalty awarded, clearly unhappy that players are being rewarded for making the most of minimal contact in the box.
"I’m amazed that a penalty was given in the first half. I can’t believe that we’re allowing those sorts of penalties to be awarded," Moyes told Sky Sports after the game.
"We weren’t clinical enough at times. We missed a couple of really good opportunities to get another goal.
"In a lot of games we feel we can challenge. We go into many games thinking we’ve got a chance. I wouldn’t say we were unlucky today, but I’m really disappointed when we were 1-0 up that the penalty was given."
Speaking to BBC Match of the Day about the penalty, Moyes added: "It’s not the sort of football I want to be involved in. 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 the decision [Diogo Jota’s disallowed goal] went for us, but the first-half one didn’t."
The penalty would prove decisive as Jurgen Klopp's side scored an 85th-minute winner via substitute Jota, who was teed up by Xherdan Shaqiri.
Liverpool, meanwhile, have temporarily claimed top spot but will return to second should Everton defeat Newcastle on Sunday.