Wenger’s team crashed to their second defeat of the season at Norwich on Saturday as Grant Holt punished a mistake from Gunners goalkeeper Vito Mannone to score the first half winner.
The north London outfit have won only three of their first eight league matches and are now 10 points behind leaders Chelsea.
They are also in danger of losing touch with the top four in the race for Champions League qualification after a first defeat against the Canaries since 1992.
“The gap at the top is unpleasant,” Wenger said. “We had an opportunity to close the gap but we didn’t.
“It does worry me but what is more disappointing is we didn’t score.”
Despite a disappointing display by striker Lukas Podolski and the Gunners attack in general, Wenger insisted he would not necessarily be dipping into the January transfer market for a new striker, although he was critical of his forwards’ efforts.
“We will wait until we see how players are when they come back. We did not create enough that is for sure,” he said.
“It was a poor collective offensive performance, although we have scored goals up until now.
“We have to give Norwich credit because they were very strong and organised and they stopped us very well.”
Wenger admitted Arsenal were caught out by Norwich’s intensity and struggled to find a way back after Holt’s 19th minute finish.
“I believe we have to face the reality of the Premier League and if you are not ready from kick off then you have no chance,” Wenger added.
“What can I do now? I am angry because we have not created very much.
“We were not in the game for the first 20 minutes and they scored and it made it difficult. We had to equalise before half time and did not do that.
“There was always something missing – defensively we were not at our usual level.”
Arsenal will look to get back to winning ways in the Champions league on Wednesday when they take on Schalke who won impressively in the Bundesliga against champions Borussia Dortmund.
“It was a great result for Schalke in Dortmund and a good performance,” said Wenger. “We will see how things are on Wednesday.”
Norwich manager Chris Hughton was delighted to finally secure his first league win as City boss.
Hughton admitted he had been feeling the pain after suffering four losses and three draws in the opening seven matches.
“It hurts and it take a little while to get it out of your system each time,” Hughton said. “But the defining thing was in the four games we lost, we had we played very well so we knew it was there.
“That said I will sleep easier this week that is for sure. It is certainly a better feeling after winning.”
Hughton is convinced City’s strong team spirit can keep them in the top flight despite their slow start.
“Morale has always been good and what probably helps is even though we have not picked up many points there has always been a group of teams round us so we have not been separated,” he added.
“We know where we are. We know we are going to lose games but it is about being tough and being able to bounce back.
“They are a good group, a tough group and a spirited group and we will need that as the season goes on.”