The Portuguese superstar opened the scoring after his penalty was saved and the game was poised at 2-1 when he left the pitch.
Alvaro Morata replaced Ronaldo with 20 minutes to go and were Juventus a man down, thanks to Rodrigo Bentancur's sending off in the 55th minute.
Pirlo told Sky Sports Italia: "I think it was the first time he was happy to be subbed off.
Cristiano Ronaldo subbed off for the final 20 minutes of a must-win game for Juve! :eyes:
It's not too often that you see Ronaldo head to the bench early in a big game :open_mouth: pic.twitter.com/VdjxiGWClS
- Premier Sports :tv: (@PremierSportsTV) May 15, 2021
"We were one man down, and he'd have been chasing shadows. He was happy and smiling in the dressing room."
While Pirlo insists Ronaldo was happy at coming off, footage from the game shows him looking rather disappointed at leaving the pitch early.
Romelu Lukaku equalised for Inter with a penalty after Ronaldo's opener, but Juan Cuadrado quickly restored the home side's lead.
Bentancur was then sent off in the second half to ensure a nervy half-hour or so.
Inter did get an equaliser after Giorgio Chiellini bundled into his own net with just seven minutes left to spare.
However, Cuadrado once again stepped up to rifle home a penalty of his own in the 88th minute to keep Juventus' Champions League hopes alive.
Marcelo Brozovic was sent off in added time to ensure both teams finished with ten men.
He was quick to point out post-match that his side have managed to turn up for big games against their rivals this season.
Per BlackWhiteReadAllOver the Italian said: "We've asked ourselves many times what we've lacked this season.
"We didn't have the same fire burning inside. We had to turn the light on again to fight the title and a top-four finish. The lads have proved they are up to the task in big games.
"This group has a lot to give, we have many young players, but playing for Juventus means having more responsibility. It takes time to adapt.
"We shouldn't have dropped so many points, but this is a good team, we have room for improvement, there is a good base to work well."
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