A goal down at halftime to Matty Cash, Arsenal fought back after the break through Leandro Trossard before Emi Buendia struck Villa's winner on 95 minutes.
Afterwards, a floored Arteta said: "In the manner the way we lost it was difficult to take. We had moments in the first half and after that we started to control the game and had good situations.
"We didn't manage the ball well when we regained it. We started well in second half, scored, we were dominant. Then we had periods where we gave the ball away which could've cost the game before the actual goal. It is painful.
"The manner we played, the moment someone beats his own man the space is open, we had our moments but they are a good side. We were close a few times. We need to lift up and go again.
"Every week will be like this. We are 18 games unbeaten and the margins are so small. We have to focus on ourselves and certain standards today - individual levels weren't there in some cases. We have to go again."
Arteta also remarked: “Very painful, especially after all the effort in the match. It was an open game, congratulations to Villa they are a really good side. We conceded a big chance in the first half with Ollie Watkins' goal.
"We had some dominance in the second half and I had the feeling we were going to win the game so to lose it in the manner we did is painful. Eighteen games unbeaten, you lose a game and that's what it is, this is football.
“It is what it is. We had a big chance when Declan (Rice) put the ball across for Noni (Madueke), they win a throw-in at the other end and get the goal - that’s football and the quality of this league."