The friendly, played at Optus Stadium as part of a tribute to the late Franco Baresi, finished level after Federico Dimarco's early second-half opener was cancelled out by a Christopher Nkunku penalty in the closing stages.
Amorim, taking charge of his first Milan derby, said the performance offered encouraging signs despite widespread rotation across the squad.
"I think you can see how we try to move the ball quickly. We're trying to build well from the back, without taking the risks we saw against Celtic, when we lost the ball a lot," he said.
"We can improve a lot physically, but I think we played well overall."
Asked where he wanted his side to improve most, Amorim pointed to ball retention as the priority.
"In everything. Starting with control of the ball: the more possession we have, the less we risk. But it's something we need to work on: looking back at this game, I think we need more possession to control the match better."
He also credited the foundations laid by his predecessor when asked about Alexis Saelemaekers's early sharpness.
"They're all great professionals, last year they were coached very well by Allegri and it shows," he said. "But we're talking about half an hour: at the start of the second half we were tighter, we wanted to press much higher and we changed the way we played."
Amorim's heavily rotated line-up included places on the bench for close-season signing Ardon Jashari, along with a first pre-season cameo for Rafael Leao since his return from the World Cup; the winger came on for the final half-hour and burst through Inter's defence late on, only to be denied by goalkeeper Provedel.
Milan face Chelsea in a friendly in Jakarta on Saturday, three days before Inter Milan's own rematch with Juventus, also in Perth, as both Milanese clubs continue building towards the new Serie A season.