Laurent Koscielny began the match as skipper but was forced off at half-time with an Achilles problem and it was not clear who took the armband after the interval.
Neither club captain Per Mertesacker and occasional deputy Petr Cech were in the matchday squad and asked which player will be given the responsibility for Wednesday’s Premier League game against West Ham, Wenger replied: “I don’t know, maybe you?”
Pushed to clarify who was captain once Koscielny left the field against City, Wenger added: “I don’t remember.
“No, it is a good question. Nobody asked me who is captain. I will have 24 hours to think about that.”
The exchange will reinforce the view among Arsenal’s critics that the team lacks leadership, although Wenger has never placed great stock in the importance of captaincy in football.
It is understood that the Premier League will remind Arsenal of their requirement to name a designated captain, but will take no further action aside from that.
Mertesacker was given the armband in pre-season despite suffering a serious knee injury and Arsenal captains have made a total of just 13 Premier League starts since the beginning of the 2013-14 season.
“The captaincy is overplayed, without a doubt,” Wenger said in February 2010. “You have to make an instant decision in a very quick time. The captain has no time to interfere with the individual decisions of the players on the pitch. Maybe in some other sports like rugby the captain has a bit more freedom and importance than in football.”
Believing the heightened significance of a captain to be a British idiosyncrasy, Wenger added: “Maybe it has historical roots in battles and fighting. Certainly the captain had always traditionally in the history of England a big role and a big importance.
“I like that but team sport is linked with recent history, the 20th century. Before you had no team sport, it turned up with democracy. Before that, it was all fighting and so maybe it is linked with historical roots.”
A handful of protesters attended Arsenal’s London Colney training ground earlier in the day to voice their opposition to the offer of a two-year contract extension to Wenger but the 67-year-old added: “It is three guys. Honestly. Why should I waste energy on that. Honestly.
“I don’t know what to say. It is good that they can waste their day like that.”