The Gunners suffered their fourth defeat in eight matches and have lost their last three home matches, sat ninth in the Premier League approaching the midway point in the season.
Ljungberg, 42, spoke to reporters after the game and said: "It's a great honour to do this, but Per [Mertesacker] is doing two jobs. I've said it [the managerial situation] needs to be cleared up, and it would be good to make a decision regardless of what it is."
The former Arsenal midfielder took over as a temporary successor to Unai Emery after he was sacked in November—Ljungberg has won once, lost twice and drawn twice in five games at the helm.
Kevin De Bruyne scored two goals and assisted Raheem Sterling for another as the Citizens ran rampant during the first half at the Emirates Stadium.
Ljungberg—who made 326 appearances for Arsenal—previously worked as under-23s coach and moved into the first-team coaching setup this season.
Mertesacker, 35, retired in 2018 to become the new Arsenal academy manager and is now assistant in an interim capacity, but like Ljungberg, he boasts no senior managerial experience.
It's difficult to blame the temporary leaders at all for the club's recent poor patch, and Nicolas Pepe told RMC (h/t Get French Football News) it's up to the players to improve Arsenal's form:
Carlo Ancelotti is said to be a front-runner to take over at the Emirates after Napoli fired him, though Bordeaux manager Paulo Sousa is also a target, per Tony Mogan and George Flood of the Evening Standard.
Arsenal haven't kept a clean sheet since they beat Bournemouth 1-0 on October 6, and Ljungberg has inherited a defence lacking in confidence, via Soccer AM:
It's clear someone with experience is needed to steady the ship in north London, though one must assume Arsenal's board are taking their time in an effort to make the right long-term appointment.
Ljungberg appears more desperate than that and is eager to see someone qualified take charge of the club he loves, with Arsenal's next test being a trip to face resurgent Everton on Saturday.