Keown insists Arteta cannot another season ending empty-handed.
He explained on talkSPORT: "I know it's an obvious thing, they have to win a trophy this season.
"I don't know what the consequence of that will be if he doesn't. But they have to win some sort of trophy.
"I do feel that there has been progress. Two involvements in the Champions League, got to the semi-finals last year, so we know that's good progress. But no trophies.
"You're seeing Newcastle, (Crystal) Palace winning trophies for the first time in many years. Arsenal need to do the same."
Keown also said: "They're definitely going to challenge this season. But the Arsenal fans will cry out for a trophy.
"I don't think we've reached the stage yet of the Arsene Wenger years, where I felt like he was almost like an individual stood at a fruit machine, knew it was going to pay out, and wouldn't remove himself from the machine until it did. Because eventually, he did actually win a trophy.
"I don't think we've reached that stage. He's still progressing, large parts of last season without a striker.
"We don't want any excuses anymore. Now he just needs to be positive. You got lucky a little bit yesterday, but that's good. You need luck if you're going to be champions. One step at a time."