David Raya, Jurrien Timber, Ricardo Calafiori and Gabriel Martinelli all came off with cramp during the second half at the Etihad, leading to accusations of timewasting.
But Arteta said the Gunners will be without injured players for Wednesday’s EFL Cup tie against Bolton.
“I always prefer facts over words or fiction,” Arteta said.
“Let’s see who’s available tomorrow and then we can talk about the dark arts or some of that.
“Unfortunately, yes, some players will not be available.”
Asked if any of the injuries he suffered against City were serious, Arteta said: “We have to wait. One of them.”
Trossard’s second booking at the Etihad came when he gave the ball away after a foul on Bernardo Silva.
It is the second time this season an Arsenal player has been sent off for such an offence, with Declan Rice being sent off against Brighton in August.
Asked if he needed to warn his players about the rule, Arteta said: “You mean passing the ball? I think so… just leave the ball, don’t touch the ball. We play without the ball.”