Despite having plenty of the ball, the Gunners - who included England midfielder Jack Wilshere in the squad after more than a year out with injury - were lacklustre as Grant Holt's scrambled effort on 20 minutes following a mistake by keeper Vito Mannone proved enough for all three points to move the hosts out of the relegation zone.
Wenger accepted Arsenal - who have now lost two from the last three league games and are 10 points behind Premier League leaders Chelsea - were well below the usual fluent best and created very few openings as for once the Premier League's worst defence held firm.
"Norwich had a good defensive performance, were focused and committed. We had a lot of the ball, but did not create much with it, which was a disappointing performance for us," he said.
"I felt we lacked a bit of sharpness. We missed what makes the success at the top level, that is complete focus and they were sharper than us.
"We do not blame anybody, made many mistakes today [Saturday]. We have to put that performance behind us and realise that is not good enough.
"The attitude of the team has been excellent, but that was not at the level of what we have produced until now, it was the first time of the season we were way below par.
"We have to come out with a difference performance in the Champions League game (against Schalke) on Wednesday night."
Alex Oxlade-Chamberlain came on in the second half, but had to be replaced after less than 10 minutes because of a hip problem which will rule him out of the midweek European tie.
Wenger hopes Wilshere will soon be back in competitive action, probably for the Capital One Cup tie at Reading.
He said: "I would have brought him on if the game had allowed it today [Saturday], but it was too intense.
"He will play on Monday with the reserves and then we will see where we go from there."
For Norwich, there was much more a sense of satisfaction after battling to a first league win under Hughton.
The Canaries manager said: "This has been a long time coming, which our performances have warranted.
"However, this league is unforgiving.
"I am delighted for the team, because the work-rate was outstanding and there is no coincidence in the result.
"We could have caught them on the counter more and made life easier for ourselves towards the end, but overall we restricted them and so it was a very satisfactory performance.
"We have deserved this by our play this season so far, so it is a very good feeling to get the win here at Carrow Road for the supporters."
Norwich face a trip to take on former manager Paul Lambert at Aston Villa next Sunday.
Hughton added: "We will enjoy it, but once this is all out of the way, we will concentrate on the next one."