Team mate Paul Scholes was also dismissed, for a second yellow card, in stoppage time of a combative Premier League game decided by Duncan Ferguson's 55th minute header.
There was no sympathy from the United manager for Neville after the experienced international was shown a straight red.
"You can't kick a ball at a spectator, not nowadays, and Gary Neville should know that," Ferguson told Sky Sports News.
"Intimidation from supporters is always there, we had plenty of that today. It's a (Liverpool-Manchester) derby gameand you are going to get that kind of thing."
TheUnited boss was far more conciliatory towards Scholes.
"PaulScholes was sent off for a late challenge. How many late challenges were there in that game from Everton players -- it was amazing."
Ferguson also criticised match referee Phil Dowd, saying:"Everton knew it was a weak referee and they exploited that to the full. I don't blame them.
"Rightfrom the first whistle, there was no protection."
United stayed third in the table, four points behind champions Arsenal who drew 0-0at champions elect Chelsea.
The runners-up qualify automatically for the Champions League while the third-placefinishers have to go through a qualifying round.