Vertonghen and Giroud got into an off-the-ball tussle in the 37th minute of the contest, and Neville felt that both players' actions were poor.
Giroud throw himself to the floor in the penalty area, before getting up and charging at Vertonghen, only to see the Belgian defender take a tumble as well.
And Neville said: “They’re having a right go at each-other, there’s nothing wrong with that, and then it’s rubbish from Giroud. He throws himself to the ground for some reason.
“It’s rubbish from the pair of them. The linesman probably saw it and thought ‘that’s embarrassing, I’ll leave it’.”
That squabble was the only off-the-ball incident of note in what was a pulsating North London Derby, which was fiercely contested.
Tottenham took the lead in the match through Harry Kane, and they were dominant for large portions of the match, but they were unable to hold on.
Arsenal scored through Kieran Gibbs and they managed to turn the tables, with Spurs left hanging on in the end.
The match finished as a 1-1 draw, and neither side is likely to be too disappointed with the result, as it keeps them both in the upper echelons of the table.