Despite the Gunners securing all three points at Old Trafford on Sunday, the summer signing struggled.
In his 60-minute appearance, the Sweden international created no chances, took no shots, had just three touches in the opposition box, and won only three of his 13 combined ground and aerial duels.
"I think there are seven, eight situations when the ball is completely open to play through and we are in and attacking the keeper. We give the ball away and then it becomes a basketball game," Arteta told the media.
"Well, he did a lot of things very good. You can tell especially in our high press and rhythm that we demand, that especially in the first half we were giving a bit too much time. It is something that we have to work on him, especially there.
"Then in the final action situation, he did not have that many chances to do that, because in the previous action, we had to play that last ball and the last was standing still with 40 metres to play.
"We did not manage to put the ball through to exploit his quality. But overall, coming away to Man United, winning your first game with Arsenal, is a good start."