The Gunners had chances to secure three points and keep their hopes of Champions League football alive but they were unable to find a breakthrough on the night.
Arteta told Sky Sports News: "It was two points that got away. It was a big battle and we had the better chances and better play. We were unlucky not to score.
"When we had our chances we didn't hit the target and that's why we didn't get the points. The pressure is on every team, Chelsea and Spurs have got tough games coming up."
Arsenal are third in the Premier League but are only two points ahead of fourth-placed Chelsea and fifth-placed Tottenham Hotspur, who both have games in hand.