The 35-year-old was shown a yellow card just before half-time at Goodison Park after he threw himself to the ground in an attempt to con referee Andre Marriner.
"It was a stupid thing to do," said Neville. "I don't often find myself in that position and I thought [Reds defender] Daniel Agger was going to take me out.
"But I got a good kick up the backside at half-time as I couldn't commit to tackles in the second half.
"I'll take the rollicking and I won't do it again, that's for sure."
Moyes, who in the build-up to the match expressed his concern that diving was ruining English football, added: "I said to him it's completely wrong, you don't do that."
Neville has received four yellow cards in 11 appearances so far this season.