After the news was confirmed that Emery was the unanimous choice ahead of Mikel Arteta by the Gunners hierarchy, Wright admitted he's thrilled with the appointment.
However, the club legend felt their public pursuit of Patrick Vieira was disgraceful, given the circumstances of having no intentions of hiring the former France midfielder.
"It was disgraceful the way that was handled," Wright told Sky Sports. "You can't phone up a legend like Vieira - for what? For tokenism? Was it the Rooney rule? It's embarrassing.
"If you are going for Emery or Arteta, just go for them. Don't go and give Patrick a phone call. How does Patrick feel now?
"I don't take anything away from the fact that we've got a new man. I'm really happy. Arsenal fans are really happy from what I've seen so far."