The Welshman starred for the Blancos in the absence of Ronaldo - who missed out through injury - as the 24-year-old headed the hosts into the lead, before setting up Karim Benzema to double the advantage.
Bale hit a further two goals with either foot to complete the 'perfect' hat-trick but, despite admitting that the former Tottenham Hotspur star is "on the right track", the Brazilian feels that Ronaldo remains in a league of his own.
"You cannot compare Bale and Ronaldo," he told reporters after the victory. "Cristiano is above the rest of the players and everyone on the team knows that. Bale is a great player, though, and he is on the right track."
The Portuguese is expected to be named among the three-man selection for the Ballon d'Or having hit 66 goals for club and country in the calendar year - including seven hat-tricks.