Neville described Arsenal as displaying “a little bit of immaturity” while Carragher said they should “just get down the tunnel” as captain Martin Ødegaard took pictures of the club’s photographer with his camera.
Liverpool midfielder Curtis Jones also accused Arteta of “stealing” Jurgen Klopp’s fist-pump celebration when acknowledging the crowd at full-time.
“They can have their moment and stuff, but there’s a long way to go,” Jones said of Arsenal, who travel to West Ham on Sunday.
Arteta twice won the Premier League with Manchester City as an assistant coach under Pep Guardiola.
When asked whether there was any correlation between a team celebrating one victory and their durability for a title race, Arteta told a news conference on Friday: “If I think when I have won Premier Leagues somewhere else, the answer would be ‘big no.’
“Because I have experienced it. That’s it. My experience says no but maybe someone says ‘my experience, yes.’ Mine says no because I have seen how to celebrate.
“I love it — I’ve seen [away] managers at the Emirates on their knees, on the pitch. I’ve seen very big managers walking onto the pitch, I’ve seen managers going across the touchline. I’ve seen that all in the Premier League.
“Personally, I love it because it brings such passion and emotion to the game. When it’s done in a natural and unique way, I think it’s great. It’s my opinion and a lot of people may have something very different to mine.
“I see a lot of games and in game three, game six, game eight, there are managers and teams celebrating a lot, fans celebrating a lot. It’s so tough to win in this league.
“For sure, it was a big match for us. You can tell how much it meant from the [first] whistle. You could sense the stadium and the atmosphere very different already. It was a great day.”
Arsenal expect Bukayo Saka to be available against West Ham after being forced off late in the second-half against Liverpool with a foot problem while Gabriel Jesus (knee), Oleksandr Zinchenko (calf), Takehiro Tomiyasu (calf) and Thomas Partey (thigh) are being assessed.