Arteta's insistence on playing out from the back was questioned once again on Thursday night during the Gunners' 3-1 Europa League win over Olympiacos.
Dani Ceballos was the latest culprit in a run of mistakes from Arsenal players which have led to opposition goals. The Spaniard lost the ball under pressure after a pass from goalkeeper Bernd Leno, with the Greek side taking advantage by firing in an equaliser
It comes just days after Granit Xhaka inexplicably tried to chip Burnley's Chris Wood in his own penalty box, with the ball instead ricocheting off the striker's midriff and into the net to gift the Clarets a point in a 1-1 draw.
Arsenal have conceded eight shots on their goal directly from errors in the Europa League this season, three more than any other side.
And Keown believes continued mistakes at the back, especially from German goalkeeper Leno, will result in an early exit from the competition.
"You want to play from the back and you don't want to create fear in your players," he told Jim White on talkSPORT.
"But, at the same time, you don't want them to make mistakes. You've got to get that balance right and, at the moment, Leno is a player where there are question marks and microscopes on him now.
"[Emiliano] Martinez was allowed to leave and go to Aston Villa and if you think about the back end of last season where Martinez came in, was that the difference?
"They went on to win the FA Cup, he played in the Community Shield final.
"It will cost Arsenal, ultimately, in this competition if they don't learn to stop making silly mistakes."
The Gunners were ultimately saved in Athens thanks to a power header from Gabriel and a rasping shot from Mohamed Elneny to somewhat paper over the cracks.
Arsenal took the lead from an emphatic finish from Martin Odegaard - his first for the club - and fans will have hoped the Real Madrid loanee would offer more in the game, but it appears the midfielder still requires time to settle.
But Keown says the Gunners already have a better player in that attacking midfield position in their ranks - 20-year-old Smith Rowe.
The youngster is currently struggling with a niggling injury and made an eight-minute cameo against Olympiacos having started on the bench.
And Keown expects him to go straight back into the starting XI in Odegaard's place once he regains full fitness.
"I still think Smith Rowe is a better player in that position," Keown said. "But clearly he is injured.
"I think Odegaard is an interesting player; just listening to him after the game, I think he doesn't really have a great deal of confidence.
"That shot he had demonstrates the quality he possesses, he missed an early opportunity and he showed, again, character.
"I was watching him closely after that to see if he was really up for it. When you make a mistake like that, you can kind of suffer a bit.
"But he hit an amazing shot from distance and maybe this is the start of something big for him?
"But to take over from Smith Rowe is another level, because he is a very special player."
Martin Keown believes Emile Smith Rowe is better than Martin Odegaard and suggested Mikel Arteta 'creates fear' in the Arsenal defence with his tactics.