But 95% of Newcastle fans agreed with Neville, describing the performance as "RUBBISH"!
Carver was furious at comments made by the Match of the Day pundit in the wake of his side's 3-0 surrender at Goodison Park last Sunday in which he voiced the opinion that some members of the Magpies squad "had their flip-flops on."
The 50-year-old said: "I was pretty angry when I heard it because he couldn't be any further from the truth.
"I think it's insulting and I think it's wrong, especially from ex-players. I'm sure if they were playing now, they wouldn't like the comments, as I didn't.
"What I did do was to inform the players about what these people had been saying. I thought it was important that they knew. Now it's down to ourselves to show those people out there that we've not got our flip-flops on -- although we might today, because it's sunny!''
Carver will attempt to disprove that theory on Saturday when Arsenal visit St James' Park on the back of their midweek Champions League exit despite a 2-0 victory in Monaco, although he will have to do so with his squad having been reduced to the bare bones.
Indeed, he will have only 13 fit outfield players from which to select his team, and just one specialist central defender following skipper Fabricio Coloccini's unsuccessful appeal against his red card on Merseyside.
He said: "The good news is that I've not got a selection problem tomorrow because I've only got 13 fit senior players, plus two keepers, so that won't be too difficult.
"There's no sign of anyone coming back in the near future other than Mehdi Abeid, who is a week or so away. We're working on Rolando Aarons, everyone else is more or less long-term.
"Siem de Jong went outside for a workout for the first time today, which was nice to see.''
Meanwhile, Carver defended the decision to challenge Coloccini's dismissal for a foul on Aaron Lennon despite the outcome.
He said: "I spoke to some well-known people in the game and they all said it was a yellow card. It wasn't just out of hope, we genuinely thought we could overturn it."