Arteta took charge for the evening with Pep Guardiola serving a touchline ban for being sent-off in last season's quarter-final exit to Liverpool.
And Guardiola could only watch on in horror as Lyon punished a sloppy first 45 minutes from the pre-tournament favourites through Maxwel Cornet and Nabil Fekir.
Bernardo Silva pulled a goal back in an improved second-half performance, but couldn't prevent City slumping to their first defeat of the season.
"When you are not at the races at the start of a game in the Champions League after, it doesn't matter how good you are, it is too late," said Arteta.
In contrast to their stunning domestic form, City have now lost their last four Champions League games.
A decade into their stewardship, winning the competition for the first time may remain the holy grail for City's Abu Dhabi owners.
But it seems City's fans still need to be convinced with plenty of empty seats dotted around the Etihad and the Champions League anthem again booed before kick-off.
That flat atmosphere transferred into a City first-half display riddled with uncharacteristic errors.
"Obviously, the ideal scenario is to have a full stadium every time and to have people supporting and getting behind the team like crazy," added Arteta.
"I wouldn't like to use that as an excuse because we had this type of crowd in Champions League before and we were able to win the game."
Lyon have won just two of their opening five Ligue 1 matches of the season, but pounced on City's sloppiness.
"We need to be capable of repeating this performance in order to fulfil the objectives we have," said Lyon coach Bruno Genesio.
"The end of the game was tougher as they brought it back to 2-1 and brought on talented players. I suffered as I was scared they'd score a second goal.
"We would have taken 2-2 before the match but given the way the game went we'd have been disappointed not to leave with the three points."
Some calamitous City defending gifted Lyon the perfect start as Fekir's low cross should have been easily cut out by Fabian Delph at the back post. However, the England international swiped at fresh air and Cornet gratefully slotted into the far corner.
Guardiola's ban meant he wasn't even allowed into the dressing room at half-time, and Arteta's team talk got an awfully lot tougher two minutes before the break when long-time Liverpool target Fekir drilled a shot from 25 yards into the bottom corner.
Arteta surprisingly resisted the temptation to make changes at the break despite having a cavalry of Leroy Sane, Sergio Aguero and Riyad Mahrez on the bench.
And it wasn't until Sane and Aguero were summoned before the hour mark that City started to threaten.
By that point, it should have been too late as former Manchester United winger Memphis Depay hit the post with just Ederson to beat on another threatening Lyon counter-attack.
Sane's introduction moved Bernardo Silva into the central role where he has shone in recent weeks in the absence of Kevin De Bruyne and the two combined to get the hosts back into the game 23 minutes from time.
The German got to the by-line and his cut-back was swept into the far corner by the Portuguese international.
Anthony Lopes twice denied Aguero and Sane fired off target when well-placed in stoppage time, but Lyon held out to leave City with plenty of work to do in Group F to progress.