Arteta called it their "worst game of the season" after Arsenal failed to capitalise on an early lead and lost their second straight game, ending the year fourth after being top of the table at Christmas.
"Painful and sad day, that's how I would sum it up... we simply weren't good enough," he told reporters.
"We could not control the direct play. It was so easy for (Fulham) to win that first, second ball and have opportunity to run, and we conceded (two goals that way).
"What happened today cannot happen again. Because if you do that you will never have the chance to be where we want to be."
The North London side have 40 points after 20 matches, two behind leaders Liverpool who play their game in hand on Monday against Newcastle United.
"It could have been a beautiful way to end the year and finish top of the league, but these are the margins," Arteta added.
The Spaniard said the team needed to focus on improving going forward.
"We want to win games," he said.
"We have a chance to be the best in the best in the league with these players. So, they are really good and we are going to continue to work with them."
Arsenal resume their league campaign on January 20th against Crystal Palace.
