The Rossoneri were without talismanic striker Mario Balotelli for the International Champions Cup clash in Toronto and his absence was keenly felt as the Greeks cruised to an impressive win.
Inzaghi succeeded Clarence Seedorf in the Milan hot-seat last month, tasked with restoring the club to their former glories but, on this early evidence, he has much to do.
Balotelli was reduced to a watching brief after his involvement in the World Cup. The former Inter and Manchester City striker has been linked with a move back to England this summer but Inzaghi stressed there should be nothing read into his omission.
He said: “Balotelli, like the other national players, just joined the team. He has had just three training sessions. I had no choice [but to play] Mattia De Sciglio and Keisuke Honda because of the small squad, but hopefully in the next few games the other national players will also see some playing time.”
For Olympiakos coach Michel, it was all smiles, as his side coped well without their top three scorers from last season: Konstantinos Mitroglou, Javier Saviola and Joel Campbell.
Alejandro Dominguez opened the scoring just past the quarter-hour mark before substitute Dimitris Diamantakos doubled their lead with a lovely touch past keeper Gabriel after some excellent build-up play.
Olympiakos saved their best for last, however, extending the lead to three through Andreas Bouchalakis, whose bullet from 30 yards soared past substitute keeper Michael Agazzi and into the top corner.
Following the match Inzaghi was surprisingly upbeat, content with excusing his team for their below-par performance.
“You have to consider we got in at two in the morning the previous night and we have been travelling the last two days from Italy to New York, so we didn’t have a chance to train,” the former stiker said.
“The players tried their hardest, but that’s the best we could do given the circumstances. We have another game on Sunday against Manchester City.
"They have had more time to train so it will be another tough game but I am just happy no one got hurt.”
The circumstances were less than ideal for Milan, but using this match as an indicator, they could be in for another long season if they fail to bring in reinforcements before the transfer window closes.
The result, however, did nothing to dampen the spirits of the large group of Milan supporters in attendance, with two fans going so far as to storm the field to take a selfie with Stephan El Shaarawy as the final whistle neared.
“I know how important these fans around the world are for us, and I am sure that Milan will be back to the level we were at for the past 20 years when we were winning a lot, and that’s what I want to do with the team,” Inzaghi said.
Both teams return to action on Sunday, with Olympiakos taking on Liverpool in Chicago and Milan facing the reigning Premier League champions City in Pittsburgh, in what could prove to be Balotelli’s first match against his former club.