The result leaves second-place Arsenal 15 points behind leaders Liverpool.
Bruno Fernandes struck from a direct free-kick to open the scoring before Declan Rice's equaliser for the Gunners in the second-half.
Arteta was later asked if the title race was over and replied: "I don’t want to say that but today the frustration is that we haven’t won our game – we know the urgency and it’s about winning every single match if you want to have any chance of doing that. I don’t think it’s the right moment to talk about that."
On United's defensive tactics, Arteta insists it was due to the performance of Arsenal on the night.
He also said: "I think he (United manager Ruben Amorim) mentioned it and it was very clear that he didn’t want to play that, but in the manner that we dominated the game, they didn’t have another choice, and then they scored a goal and capitalised on that. We were unable to score a second one."
The result was the third consecutive Premier League game that Arsenal had dropped points.
Arteta stated:"Today the efficiency we had in the last 20 metres, it wasn’t good enough, we know that. Those are big parts of a lot of things that the game demands when you come to Old Trafford and what we did was superb, but at the end, you have to capitalise on that when the team is so dominant and much better than the opposition and today we didn’t.
"Then you have to overturn a result, which we know is very difficult to do here. You have to expose yourself a little bit more because you have to take more risks and then the game could have gone their way in the last few minutes."