Starting the day two points adrift of Liverpool and Aston Villa in the rankings, the Gunners would have ended a second successive calendar year at the top of the table had they got the better of Marco Silva's men.
Arteta's men began their quest for three points on the right foot, as with just five minutes gone, Bernd Leno parried Gabriel Martinelli's strike into the path of Bukayo Saka, who quickly readjusted his feet to prod the ball home.
However, the Gunners' attacking verve eluded them after Saka's opportunistic opener, and a fired-up Fulham were deservedly level before the break, as Raul Jimenez finished from Tom Cairney's sublime low cross.
The half-time interval and raft of alterations did not pay dividends for the shot-shy Gunners, who switched to a 3-5-2 setup for the majority of the second period in a bid to rediscover their offensive bite.
Such an alteration did not have the desired effect, though, and the Cottagers nicked their winner from a set-piece, as Arsenal failed to clear their lines from a corner and could only watch Bobby Decordova-Reid smash the ball into the roof of the net from close range.
Arsenal's efforts to salvage a point or three from the London derby were incredibly futile, as the Gunners did not have a single shot on target in the second half, where their best opening saw Saka balloon a volley high into the air from a promising position.
An off-colour Arsenal end 2023 with just four points to show from their last 15 on offer in the top flight, also being beaten by Aston Villa and West Ham United in that sequence, and they occupy fourth place in the rankings as a result.
Sunday's defeat also marks the first time since New Year's Day 2022 where Arsenal lost a Premier League game after scoring first, having gone down 2-1 to Manchester City on that occasion, and Arteta had nothing positive to say about his side's display in the capital.
"Really tough day. A sad day. Three days ago [2-0 defeat by West Ham] we played a game we lost that we completely meant to win it, today was our worst game of the season," the Spaniard told BBC Sport.
"The pace, the purpose we have in attack, defensively we were second best, we could not dominate and had issues because of that. We didn't do enough with that [possession] - not enough purpose speed or threat.
"We were sloppy with the ball. It wasn't good enough. We didn't deserve to win. When you have opportunities to go top of league on 31 December and now end up with a really bad feeling that is football. The lines are really thin.
"If we play like we played in the other 19 games we will be up there [in the league at the end of the season]. If we play like today we will be nowhere near. Today was a really difficult day to swallow."
When asked by Sky Sports News whether the answer to their struggles could present itself in the form of January signings, Arteta replied: "We have to do what we did in the previous 19 games. With the same players."
Before Arsenal's first Premier League game of 2024 - which comes at home to Crystal Palace on January 20 - the Gunners will commence their bid to win a record-extending 15th FA Cup when they host Liverpool in the third round on January 7.