The former Bologna man was confirmed as Arsenal's second permanent signing of the summer on Monday evening, joining in a deal that could eventually reach up to £42m.
Calafiori had already joined up with Arsenal's pre-season squad in the USA before his transfer was officially announced, leading to some optimism that he might appear against Liverpool in Philadelphia.
However, the Euro 2024 star did not make the squad at Lincoln Financial Field, as the North London giants suffered their first defeat of pre-season courtesy of goals from Mohamed Salah and Fabio Carvalho.
Speaking to the media after the game, Arteta was asked whether Calafiori could be seen in an Arsenal strip in the coming weeks, but the Spaniard affirmed that the defender needs more time to acclimatise to life at the club.
Arteta: 'We will have plenty of time to see Calafiori'
"We had to manage him. He had a very busy 48 hours before he took his flight and joined us here, and then it was the jetlag, it's a lot of things," arsenal.com quotes Arteta as saying.
"He hasn't trained with the team yet and we want to build him up slowly to get to know him first. We'll have plenty of time to see him."
Despite Calafiori's absence, and a wealth of other Euro 2024 stars still unavailable as well, a strong Arsenal lineup against Liverpool still featured the likes of Martin Odegaard, Gabriel Magalhaes, Thomas Partey and Gabriel Jesus.
The Gunners started brightly before Liverpool began to turn the screw, and the Reds were inspired by Harvey Elliott, whose slick through ball set Salah away to coolly finish in the bottom corner past Karl Hein.
The former Fulham starlet registered his second assist of the contest just 21 minutes later, as a delightful passing sequence ended with Elliott lifting the ball above the Arsenal backline for Carvalho, who converted with panache.
Arsenal reduced the arrears before the break via a Kai Havertz tap-in, and the Gunners were in the ascendancy for most of the second half, but they failed to make their dominance count as Arne Slot got one over Arteta.
"Today was a really strong test. I think we started the game fantastically well. I think after six or seven minutes we should be 2-0 up. Then we lost control, especially with two things that we didn't do well enough and we allowed them to run in transition, which is a really dangerous thing to do against them," Arteta said.
"And in the second half we improved a lot and we deserved more. But it was great, really difficult conditions to play. Great crowd and we've got a lot out of it so I'm really pleased."
What next for Arsenal after Liverpool defeat?
With their transatlantic tour now complete, Arsenal return to the English capital to prepare for their last two friendlies of the summer, the first of which sees Bundesliga champions Bayer Leverkusen visit the Emirates on August 7.
Four days later, Arteta's men host Lyon in the latest edition of the Emirates Cup, ahead of their opening Premier League fixture against Wolverhampton Wanderers on August 17.