United were 2-1 winners at the Emirates Stadium to move above Arsene Wenger's side in the Premier League table on Saturday.
Arsenal lost by the same scoreline at Swansea City before the international break and are down in eighth place after the first 12 top-flight games.
Captain Arteta felt the defeat was harsh on Arsene Wenger's side, but realises they must make the most of their dominance in matches if they are to challenge for honours.
"I'm shocked," said the former Everton man. "I think we played our best game this season in terms of what we demand of ourselves – the quality in the way we attacked, how we won the ball back, how consistent we were throughout, the amount of chances we created.
"When you are in the box and you can't manage to score in that many situations, you can't expect to win.
"It’s not fair for the players and the fans. How can I explain the result? I can't.
"I am shocked and frustrated because we did not deserve this result considering the opposition we were playing against.
"I can only put it down to bad luck on the first goal which totally changed the game, at a time when we were absolutely controlling and hammering United.
"After they took the lead we had to take more risks to try to get back into the game and United have the players up front to cause you problems at any time.
"But I feel so sorry for the lads and for our supporters because they were terrific and I don't think we deserved this result."
He added: It’s [a lack of] ruthlessness, for sure. When you are in the box and you can't manage to score in that many situations, you can't expect to win."
