The United boss suggested that he would rather play 63-year-old goalkeeping coach Jorge Vital than the forward and Ferdinand believes that Rashford will have to leave the club after his professionalism was questioned in such an explicit manner.
Speaking on his YouTube channel, the former Red Devils defender said: "If I was the player the manager said that about, my heart, my pride, my ego - it's embarrassment.
"For someone to question your application, to question you giving 100 per cent for the team, saying you're lacking effort and taking shortcuts, that's a damning comment. There's no way back for Marcus after that.
"If he did come back that means other players can take their foot off the gas and have a way back into the team and take shortcuts."
Ferdinand believes that Rashford would have come out and responded publicly to Amorim's remarks if he felt they were false.
The TNT Sports pundit said: "For me, if it isn't true, I'm coming out all guns blazing. I'm holding a press conference and saying, 'I'm not having anyone say that about me'.
"You only do that if you are 100 per cent sure that nobody can say you're taking shortcuts. We're in an era where you have the ability to really communicate with the fans directly so the story is not getting twisted.
"I would love to sit across the table from Marcus and look into his eyes and see if he could say that. If you can't, you have to look at yourself."