Lewis Grabban’s late winner gave the hosts a deserved 1-0 third-round win against the slapdash Gunners.
The 14-time winners suffered an early exit without managing a shot on target at the City Ground on Sunday.
It was their first third-round defeat since losing 4-2 to Forest in 2018 and Arteta insisted he expected better.
“We needed more drive, more hunger to win at any cost in every single action, much more. We were not at our level,” he said.
“I’m really disappointed with the performance, first of all. Not with the attitude but how much purpose we have and what determination we showed to change the game when it’s difficult to play against and the way they play.
“I have played in games like that for the last 18 years and I know how complicated it is to come here and it’s no surprise the difficulties you are going to face. But when we do that, we have to face it in a different way.
“It is really hurting. It is a competition that is very related to our history and to get out of it is a big bump.”
Aside from a five-minute spell in the second half it was an instantly forgettable game until Grabban struck with seven minutes left.
The first half’s only moment of note was Nuno Tavares being hauled off for Kieran Tierney after 34 sloppy minutes and tossing his gloves away.
Philip Zinckernagel forced Bernd Leno into an early second-half save and the goalkeeper was equal to James Garner’s 30-yard free-kick.
In between, Eddie Nketiah wasted Arsenal’s best – and only – chance when he completely miscued a free header at the far post.
It was to prove costly as Grabban climbed off the bench to score his 11th goal of the season.
Albert Lokonga lost the ball in midfield and Ryan Yates scampered down the right to deliver a perfect cross for a stretching Grabban to convert from six yards.
Forest boss Steve Cooper took over in September when Forest were bottom of the Championship and they are now ninth and six points adrift of the play-off places.
They now host holders and East Midlands rivals Leicester in the fourth round, yet the former Swansea manager bristled at suggestions he had turned the club around.
He said: “I don’t like it when people say it because how can you say we’ve turned it round? This club has a lot of work to do and a lot of progress to be made. We are going OK but let’s not get too ahead of ourselves.
“The players have to believe they belong at this club and can be successful. We all want it and we have a lot of work to do in so many areas of the club but moments like this will only add to the belief.
“There will be some bumps in the road, setbacks, losses, poor performances – that’s just the nature of it.
“It’s part of the journey and becoming the team we want to be.
“I did feel comfortable. Someone asked me if it must have been a long seven minutes after we scored. I’ve had longer seven minutes. I mean no disrespect, the players were really engaged with what it took to win.”