The Italian side were magnificent in the opening 45 minutes, going in 3-0 up at the break having opened up a woeful Liverpool defence at will.
English champions City started their big close-season signing, Norway's Erling Haaland but, in contrast to Nunez, he had a disappointing debut, missing several chances and struggling to combine with his new team mates.
The Champions League final, which Real Madrid won 1-0, was delayed by more than half an hour after police tried to hold off people trying to force their way into the ground. Some fans, including children, were tear-gassed by French riot police.
The final between Liverpool and Real Madrid kicked off with a 35-minute delay after police tried to hold back people attempting to force their way into the Stade de France without tickets, while some ticket holders complained they were not let in.