Betis punished a series of defensive errors to score three times in the first half through Rodrigo Riquelme, Nelson Deossa and Pablo Fornals, with Arsenal responding through Piero Hincapie just after the half-hour mark.
"Very upset, given a hard time. They are fuming, but this is good. That's what we need," Arteta told reporters.
"There are things to improve obviously, some positives to take from the game and then a bad result sometimes it's good to create even more fire in the belly."
Arsenal were without several key players including Declan Rice, Bukayo Saka, Eberechi Eze and Noni Madueke, while Martin Odegaard has only recently resumed individual training.
The Premier League champions fielded a strong line-up, however, with Viktor Gyokeres, Kai Havertz and new signing Christos Tzolis all starting the match.
Midfielder Louie Copley suffered a knee injury shortly after coming on as a substitute and Arteta was concerned the 19-year-old may have sustained serious damage.
"Quite worried to be fair for the kid because the mechanism doesn't look very positive and the symptoms that he already has," the manager said.
"So we are going to have to wait and see for tomorrow's scan. Touch wood that is not a bad one."
Arsenal begin their Premier League campaign against Coventry City on August 21.