The Gunners missed the chance to re-claim fourth spot ahead of Tottenham, who beat Burnley 1-0 on Sunday.
As a result, Tottenham will head into the final day in fourth, two points ahead of Arsenal plus superior goal difference, with Spurs taking on bottom club Norwich City.
Arsenal, who have lost their past two league games, host relegation battlers Everton on the final day.
“We need to win and we need a defeat from them, and we know that in football, thats always possible, and if anything happens, you have to be there in order to do that,” Arteta told reporters.
“Today, you have to put your head down, swallow all the disappointment that we all feel, hopefully, and tomorrow start again.”
Ben White’s 55th minute own goal and Bruno Guimaraes’ 85th minute strike settled the contest where the Magpies had 16-11 shots and edged possession 51-49%.
“Normally, I can sit here and I can defend, but what weve done today, its not easy,” Arteta said.
“Newcastle were 100 times better than us in every department from the beginning to the end and its hard to accept to accept, but you have to accept it and thats the reality of what happened today on that pitch.”
He added: “Now we have to swallow everything, digest it and tomorrow is another day. We will still have five days to prepare that match.
“We know what we have to do. Theres not a lot of words I think that are needed after the performance tonight.”