After Kortney Hause broke the deadlock in the weekend's clash at Old Trafford, Fernandes had the chance to level the scores from the spot but sent his penalty flying over the bar.
The Portuguese playmaker insisted that he would "come back stronger" in an Instagram apology post, but his words have not gone down well with Neville.
During a Twitter Q&A session, Neville said of Fernandes's apology: "It's embarrassing! They need to sack their PR people, speak with some authenticity and get on with it.
"I'm going to go big on this in the next few weeks. They've all got these comms managers, that are creating personalities that don't exist!"
Fernandes and Man United will aim to bounce back immediately during Wednesday's Champions League clash with Villarreal.