The Premier League leaders took a 22nd minute lead from William Saliba’s header but were behind goals from Goncalo Inacio and Paulinho.
Arsenal rescued a draw when Granit Xhaka’s 62nd minute strike deflected in off Hidemasa Morita.
The Gunners will host Sporting in London next week but there has been discussion that Arteta’s side are prioritizing their Premier League tilt.
Arsenal have not won the Premier League since 2004 and are currently five points clear of Manchester City.
“We’re not (giving up on this competition) and today we had to go against a few issues that we’ve had in the last few days where we’ve lost a few players,” Arteta replied when asked about taking the Europa League seriously.
“We lost four or three or our strikers, but in this competition if you want to go through, youre going to have to go through difficult moments.
“We knew that, we are alive, everything is still to play for at the Emirates and hopefully we will play better and deserve to win the game.”
Arteta admitted his side’s performance was scrappy, lamenting both goals conceded.
“When you concede two poor goals like we did today away from home in Europe, its very difficult to get the positive result that we expected,” he said.
“I think the game had different phases, especially because we gave too many balls away, too many simple balls in our own half and we gave them hope and we gave them the capacity to go into transition moments that they are good at.
“In the moments we had to take control of the game and we lost a little bit of threat today, especially with the front players that we are missing in our frontline.
“We had some positive because we showed a lot of resilience to get back in the game, but we need to defend our box much better and we have to be in the return leg to beat them.”