As an Arsenal supporter who believes that Arsenal did indeed get robbed on that Newcastle goal, I am not a fan of this statement. For several reasons:

1. That was just one goal, and focusing on the refereeing mistakes that led to it shifts attention from the Gunners’ manifest ineptness in attack. Arteta should be more concerned about his and his players’ shortcomings than about those of the refs.
2. This statement won’t do what the club wants it to do, and indeed will probably be counterproductive. Do Arsenal really believe that the refs, and the Premier League and the F.A. more generally, can be shamed and bullied into doing better? My guess is that the side will get worse treatment for the rest of the season thanks to Arteta's whining and bitching and the club’s endorsement of it. 
3. This sets a really bad example for the players, who will be learning from their club’s leadership how to act when things go wrong for them: Don’t own your shortcomings, but blame blame blame, and do it in your loudest voice. 
4. A much better approach would be to seek collective action: talk to other clubs who are, or ought to be, angry about the shocking incompetence of the VAR system, and try to lead collective action — and lead it behind the scenes. That might not be as emotionally gratifying, but it would be infinitely more effective. 

This whole situation is very sad, because Arsenal have the most attractive young side in the league. They could easily be making fans, but instead they seem to be determined to make enemies. And if you were a transfer target, is this a club you’d want to play for? Last year the answer would have been a big Yes; now I suspect it’s leaning more and more towards No. Instead of a place of joy and excitement, it’s starting to feel like the Bruno Fernandes of clubs: talented but incessantly  and frustratingly bitchy. 

An exceptionally promising era in the club’s history just may be giving way to something much darker, and that is wholly the fault of the team leadership’s emotional immaturity and incontinence. It’s time for Arteta & Co. to shut their mouths and get better.