"It's not acceptable, and it's something I gotta figure out," Elliott told reporters after the game. "I don't know. I need to figure something out."
The three-time Pro Bowler said the loss is "on me."
The Cardinals punted on their first three possessions before Elliott's fumble set them up on their own 46-yard line. Kyler Murray eventually hit Christian Kirk for a six-yard touchdown pass as Arizona took a 7-0 lead.
Two plays later, Elliott coughed it up again, allowing the Cardinals to set up on the Dallas 27-yard line. Kenyan Drake punched it in from one yard out to double Arizona's advantage.
The Cowboys didn't want to fall behind by double digits as Andy Dalton made his first start in place of the injured Dak Prescott at quarterback. He threw 54 passes, two fewer than his career high, because Dallas needed quick scores to get back into the game.
Elliott didn't blame Prescott's absence for the result and reiterated how he "gave the ball away and gave [the Cardinals] all the momentum they need to go take off."
The Cowboys have many things to worry about amid their 2-4 start, and Elliott's fumble problems are on that list.
After Monday night, his five fumbles are the most in the NFL and three higher than the next closest running back. He has never finished a season with more than six fumbles, so he's poised to set the wrong kind of personal high in 2020.
With Prescott out, the Cowboys need to have confidence in the running back whose $15 million average salary is tied for second-highest at the position. Right now, Dallas' faith in Elliott might be wavering.