Reds centre-back Virgil van Dijk was adjudged to have fouled Erik Lamela by referee Jon Moss in stoppage time, allowing Harry Kane to net a dramatic late equaliser from the spot. Earlier in the game, Kane missed a penalty after going down under a challenge from Loris Karius.
Liverpool manager Jurgen Klopp raged against the decisions in his post-match interview, claiming they had cost his team the chance to go five points clear of their top four rivals and that the referee wanted to make himself the centre of attention.
However, Neville was adamant that Moss got both the penalty calls right.
"[For the first penalty] Karius threw himself out at it, and Jurgen Klopp won't be settled down by the goalkeeper today, and neither will the goalkeeper," the former England defender told Sky Sports.
"It was a penalty for me, it looked reckless, and the chat between the linesman and the referee is something that created nervousness amongst officials.
"[The second also] looked like a penalty from here. I shouted penalty! I've done that one myself, where you don't see the attacker coming across you, you control and then all of a sudden he's there. It just looked a clear penalty," Neville added.
"I have to say, my feeling was the assistant referee Eddie Smart, who had that nervous chat with Jon Moss earlier, could have easily said no. Moss waved it away and said no penalty, and the assistant referee gave it. That takes real nerve. I thought it was the correct decision."
Klopp said it was "really hard to take" the result as he felt his team had deserved to win the game. Mohamed Salah continued his excellent form by scoring both Liverpool goals, including a fine solo effort late in the second half.
"I am angry but I can't change things so what's my job? To create headlines? To get punished? To pay a fine? If I said what I think I would pay the biggest fine in world football. That makes absolutely no sense," Klopp was reported as saying by BBC Sport.