The 24-year-old Scot played some stunning snooker to beat Selby 13-9 and end the Leicester man's chances of retaining his Crucible crown at the second-round stage.
"I said to him that if he plays like that there's no reason why he can't win it," world number one Selby said.
"He played fantastic all match, didn't do much wrong and deserved to win."
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Selby trailed 10-6 after the morning session and lost two of the first three frames to fall 12-7 behind.
He showed his renowned spirit to get back to within three frames, but a seemingly nerveless McGill finished the match with a stylish 82.
"I probably lost it in the second session when I played really poorly," Selby, 31, said.
"But taking nothing away from Anthony, every time he got a chance he seemed to punish me.
"Over the whole match he probably only missed two long balls. He has probably played as well as anyone has played so far.
"He was either winning it in one visit or making a 50, playing a good safety and putting me under pressure."
Selby's defeat means that the 'Crucible Curse' remains, with no first-time winner having retained his title.
Shaun Murphy was the last qualifier to win the World Championship in 2005, and McGill will play either him or Joe Perry in the next round.
Deposed champion Mark Selby says qualifier Anthony McGill can go on to lift the World Championship title.