The Real Madrid forward opened the scoring for his nation on Friday night and added two more before full time, the third a sumptuous free kick to salvage a 3-3 draw in the latter stages of the game.
Mourinho, whose Red Devils have been linked with a move for Ronaldo, was full of praise for his compatriot, who has now become the first player to score in eight consecutive major tournaments dating back to Euro 2004.
"There are players for some matches, there are players for every match and there are players for special matches," Mourinho told RT. "And the players for special matches are the ones."
Ronaldo spent six illustrious years at Man United and also played under Mourinho at the Bernabeu.