Ronaldo opened the scoring for his nation in Sochi's Fisht Stadium and added two more before full time, the third a well-taken free kick late on to salvage a 3-3 draw.
Santos, who steered Portugal to the Euro 2016 title, also hailed his player's impact in rallying his teammates after falling behind against the 2010 world champions.
"Cristiano Ronaldo has incredible mental endurance, he has technical quality and an incredible mind - that is what makes him one of the best in the world," Santos told BBC Sport.
"When it was 3-2 he was the one who raised his team. He plays in great teams, is always in great finals so that gives him a different perspective."
Ronaldo is the first player in history to score in eight consecutive major tournaments for his nation in a streak dating back to Euro 2004.