Substitute Lewis Grabban stretched out his leg to convert Ryan Yates's cross in the 83rd minute and it was no more than Forest deserved at a vibrant City Ground.
Arsenal were lacklustre and could have few complaints against a well-organised Forest side who earned themselves a Midlands derby against Leicester City in round four.
Arteta's side, who face Liverpool in the League Cup semi-final first leg next week before a north London derby at Tottenham Hotspur, failed to muster a shot on target as they suffered a repeat of their third-round loss to Forest in 2018.