Tottenham remain two points above their north London rivals in fourth place in the Premier League.
Spurs now realistically only need a draw away to already-relegated Norwich on Sunday to secure a top-four finish thanks to their superior goal difference.
Arsenal's defeat also guaranteed third-place Chelsea's place in the Champions League next season.
Ben White's own goal and Bruno Guimaraes' late strike were the difference between the sides.
"A really difficult night to swallow," said Arteta. "Newcastle deserved to win comfortably. They were much better from the first minute, we had nothing in the game.
"They were much better than us in everything that a football match requires. We could not cope tonight with the game we had to play here."
Arteta's men were in the driving seat with three games to go as they lead Spurs by four points.
But Tottenham's 3-0 derby win on Thursday cranked up the pressure on the young Gunners who failed to respond.
"Newcastle were 10 times better than us and the performance was nowhere near what we need to play in the Champions League," added Arteta. "We weren't at the races."
Throughout the game, the hosts were very much in the front foot but the pressure paid dividends when Joelinton's dangerous low cross just evaded Callum Wilson and flew into his own goal off the unfortunate White.
Newcastle are firmly rooted in mid-table, but looked like the side with more on the line as they continued to storm forward.
Wilson fired over from Guimaraes' cross and then sent an audacious effort from 40 yards floating inches past the post.
In between times Ramsdale produced another big stop from a one-on-one with Jacob Murphy.
A second Newcastle goal seemed only a matter of time and it duly arrived five minutes from time when again Wilson was denied by Ramsdale, but Guimaraes swept home the rebound for his fifth goal since a January move from Lyon.