And Stubbs said: "That was a two-footed lunge. If a player leaves the ground with both feet, that's a red card, and he gets a yellow.
"In the laws of the game if a player goes in with two feet and makes a lunge, and that is what it was, it's a red.
"If Phil (Neville) hadn't been so honest he could have been rolling around and trying to get him sent off. It's a two-footed tackle and that's a red card offence."
Stubbs was also furious with referee Mark Clattenburg after the game's crucial turning point when Tony Hibbert was sent off for bringing down Steven Gerrard in the box, a penalty confidently put away by Kuyt 10 minutes before his flying tackle on Neville.
Everton were deservedly ahead from a first-half Sami Hyypia own goal at that point, and Stubbs said: "The referee went to book Tony Hibbert holding a yellow card, their player (Gerrard) walks past him (the referee) and it's changed to a red. Have a look at the replay, and see for yourself.
"We saw the replays. That's disappointing. We were 1-0 at half-time and on top, we had control of the game.
"The penalty changed everything, it gave them impetus and we were a man down. It was always going to be difficult after that with them having more of the ball and pressure. But Tim (Howard) didn't have any saves to make. We were under the cosh and wanted to see it out for a draw, I am as disappointed as I have been all season. I suppose I sensed a red card. But the replays show he had the yellow and put it back in his pocket. It was a big call."
Liverpool's injury-time winner came after Neville had handled a shot from substitute Lucas on the line, and this time referee Clattenburg had no option but to bring out the red card before Kuyt slammed home his second penalty.
Stubbs fumed: "If the referee looks at the decision again he will see the penalty appeal was right. Their lad had his arms all around Joleon, what was he supposed to do?
"And Benitez has gone on TV saying he was diving, but just look at it, that's a stone-wall penalty. The referee was close, but that means nothing. He was close to a lot of things and didn't give them.
"We are disappointed because we have lost. But there was zero feedback from the referee, I think they should have to come out after a game and explain themselves.
"We have to explain ourselves if we make bad decisions or mistakes, why not referees?"