The England international, who joined the two-time Premier League champions from Tottenham Hotspur for £50m earlier in the summer, was given his marching orders just before half time.
While carrying out punditry duties, Neville told Sky Sports News: "[Madley's] got a great view of it, he has a little look at him Kyle Walker.
"I think the referee must think he elbowed him, he must think he's raised his elbow, he must think he's made contact with him. The reality is, he hasn't. I'll slow it right down, he has a little look Kyle Walker, which I think might go against him.
"He's backing into him, the amount of times I did this as a full-back, you try and use your body to establish your position. Calvert-Lewin's gone down, he's been clever, he's been effective in the first half.
"He's held his head and that's what I think conned the referee. You could say it's clever from Calvert-Lewin, you could say it's cute. Personally, it's a soft second yellow."
Walker was making his home debut at the Etihad Stadium.