Ronaldo scored a brace and set up the other in his side's 3-3 draw with Hungary as they secured a last-16 clash against Croatia.
The Real Madrid star netted with a delightful flick and then a header for Fernando Santos' men.
But Shilton said it was dangerous for Portugal to be relying so much on Ronaldo.
"Yet another moment of individual brilliance came from Cristiano Ronaldo, of course, who is probably the best player in the world," he wrote in The Times of India.
"The unfortunate thing is that he cannot be the whole of Portugal.
"Even so, his first goal against Hungary will probably be talked about for years.
"His beautiful back-heel to the low right wing cross created a perfect finish, and his lion hearted performance is the reason his team aren't on a plane back home."
As for Portugal's next opponents – Croatia – Shilton said he was unsurprised by their 2-1 victory over reigning champions Spain.
"I wasn't really surprised by Croatia's defeat of a slightly jaded Spain, because as I have already said, Croatia is my outsider of the tournament," he wrote.