The Gunners were punished for a series of defensive mistakes during Wednesday's friendly in Dublin as Real Betis raced into a commanding first-half lead.
Rodrigo Riquelme, Nelson Deossa and Pablo Fornals all found the net for the Spanish side, while Piero Hincapie pulled one back for Arsenal shortly after the half-hour mark.
Despite the disappointing result, Arteta was encouraged by the response from his squad.
"They are very upset. They are giving themselves a hard time. They are fuming, but this is good. That's what we need," Arteta said.
"There are things we have to improve, but there are also positives to take from the game. Sometimes a bad result creates even more fire in the belly."
Arsenal were missing several important players, including Declan Rice, Bukayo Saka, Eberechi Eze and Noni Madueke, while captain Martin Odegaard has only recently returned to individual training.
Even so, Arteta named a strong starting line-up featuring striker Viktor Gyokeres, Kai Havertz and new signing Christos Tzolis.
The biggest concern from the match came after substitute Louie Copley suffered a knee injury soon after entering the game.
Arteta admitted he fears the 19-year-old could be facing a lengthy spell on the sidelines.
"I am quite worried for the kid because the mechanism of the injury doesn't look very positive and the symptoms he already has are concerning," he said.
"We have to wait for tomorrow's scan. Touch wood that it is not a bad one."
Arsenal will continue their pre-season preparations against Borussia Dortmund at the Emirates Stadium on Sunday before beginning the defence of their Premier League title away to Coventry City on August 21.
