"I couldn't do much in two days apart from giving some logic to the team. Now I need to get to know them."
Mancini said he was knocked back by the performance of 35-year-old forward Didier Drogba, who scored the first goal and set up the late equaliser.
"Drogba has been incredible," he said. "I didn't expect a performance like that. He played alone in attack, in the home of Juventus; extraordinary."
He added: "In the first half we played well, but physically we struggled in the second. I don't think Juventus are at their best at the moment, although they could be soon, it's not unusual."
Mancini had been out of a job since being dismissed by the English club in May after his team were shocked by Wigan Athletic in the FA Cup final and gave up their Premier League crown to Manchester United without much of a fight.
He spent three and a half years at the Etihad Stadium, leading City to the Premier League title in 2012 and the FA Cup the previous year, bringing an end to the club's 35-year trophy drought.