It has not been a surprise to see Arsenal over these past seven trophy-less years follow one step forward with two in the other direction. And they were at it again here, losing abjectly to a struggling Norwich side just when it appeared they were set to make a genuine assault on the title.

The shock instead came in how their manager reacted to the defeat. There was none of the typical blaming of referees, or accusations of bullying tactics by the opposition. Rather, Arsène Wenger accepted the better team had won and, raising eyebrows further, was fiercely critical in his assessment of his own side.

"I am angry," the Frenchman said. "We have to acknowledge that we did not create a lot and, overall, it is very disappointing that we were not in the game in the first 20 minutes. We gave an easy game away. There was something missing and offensively we were not at our level. Give Norwich credit, too, as they were strong, very committed and very well organised. This has been a good lesson for us but I would have preferred not to get it – too many lessons like this and you will stand at the end of the season with too many regrets."

Arsenal supporters know that feeling well, and even at this early stage of the campaign will look at the league table with a sense of disgruntled deja vu. Their team sit ninth, 10 points behind the leaders Chelsea and six off Manchester City in third place, where the Gunners finished last season.

"The gap is unpleasant," added Wenger, who celebrates his 63rd birthday on Monday. "You cannot say you don't worry about that." It would be unwise to become too gloomy about Arsenal's prospects, and certainly Harry Redknapp's claim that the team look "well short" and finishing in the top four would represent one of Wenger's "biggest achievements" appears over the top. But after such a positive start, one that saw Arsenal win at Anfield, draw at the Etihad Stadium and generally perform with a collective sense of purpose, it is deflating for those associated with the club to think this may be another campaign in which they merely make do with qualifying for the Champions League.

Certainly it is not the hallmark of prospective champions to lose against opponents who came into the game without a league win and having made their worst start to a top-flight campaign, as Arsenal did on Saturday. The visitors dominated possession – 62% compared with Norwich's 38% – but were disjointed, sluggish and created few clear-cut chances. The best fell to Olivier Giroud early in the second half, but as has been typical of the French striker since his arrival from Montpellier in June he made a mess of a close-range scissors kick following Carl Jenkinson's cross into the area.

It is during moments like those that the ghost of Robin Van Persie continues to haunt Arsenal and, perhaps tellingly, Wenger did not rule out signing another striker during the next transfer window.

"I cannot tell you that [if Arsenal will sign a striker] now," he said. "We have players out and when they come back, we will see. We did not create a lot [in this match] that is for sure."

But as Wenger himself testified, part of the reason Arsenal were so blunt at Carrow Road was because of the efforts of Norwich, whose organisation in defence and resilience throughout the side made it hard to believe that they came into this contest with only three points from seven games and having lost their last two fixtures 5-2 and 4-1.

Chris Hughton's men refused Arsenal space in dangerous areas and attacked with pace and conviction, getting their reward for a positive start after 19 minutes when Grant Holt pounced after Vito Mannone, the visiting goalkeeper, had failed to hold on to Alex Tettey's long-range shot.

The goal was Holt's third in three games and suggested that last season's top-scorer for Norwich, when they finished 12th under Paul Lambert on their return to the Premier League, is primed to be a driving force for the club once again.

"I always want to score and it is a run of games I need to feel good," said the 31-year-old. "The more that happens the sharper I get and the better I look."

The same can perhaps be said of Norwich, who will now be keen to build momentum. Their next opponents? Paul Lambert's Aston Villa.

Man of the match Alex Tettey (Norwich)