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The Gunners fell 13 points behind Premier League leaders Liverpool after dropping points again.
Arteta ideally needed his team to respond to Saturday's defeat against West Ham by beating over-achieving Forest.
His players dominated possession but struggled to create clear-cut scoring opportunities.
Injuries have decimated Arsenal's attacking options, with midfielder Mikel Merino handed another start as a makeshift striker.
Arteta said his players fell short in their attempts to win the game, having mustered only one shot on target.
The Spaniard told BBC Sport: "We dominated the game.
Arteta accepted last weekend that the title race is no longer in his side’s hands.
That was emphasised even further on Wednesday night.
Arsenal have a game in hand over Liverpool but making up the 13-point deficit now seems impossible.
Arteta said on the title race: "It was same a week ago, two weeks ago, three months ago.
The only thing we can do is win our matches and see how many points we get."
Things get even tougher for Arsenal over the coming weeks.
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