Daichi Kamada's fine second-half brace overturned Pierre-Emerick Aubameyang's opener and stretched the Gunners' winless streak to seven matches in all competitions.
A sparsely populated Emirates Stadium, where the officially announced figure of 49,419 tickets sold was hardly represented by the attendance, booed Emery and his players at full time.
Keown, who played in the decorated Arsenal sides managed by George Graham and Arsene Wenger, feels the ex-Sevilla and Paris Saint-Germain boss has run out of road – as evidenced by their "relegation form".
"I think he may well have taken the team as far as he can," Keown told BT Sport in his role as a pundit.
"We just witnessed an absolute shambles of a performance in the second half. The team selection, the team motivation, the substitutes, the performance. Everything was missing here. It was a dreadful performance.
"Is he able to motivate this team? He seems to have lost the players. The desire seems to have ebbed away."
Injuries to defenders David Luiz and Shkodran Mustafi further compromised Emery, while Granit Xhaka – back in the side for the first time since being stripped of the Arsenal captaincy – completed 90 minutes despite appearing hindered by a knee problem suffered before half-time.
Forwards Nicolas Pepe and Alexandre Lacazette looked on as unused substitutes while their team-mates unravelled.
"I could question players," Keown said. "Xhaka stayed on the pitch, perhaps should have gone off; Mustafi couldn't get off quick enough.
"The substitutions that he made, the players that are sitting on the bench. You've got Pepe there, you've got Lacazette – you're trying to get back into the game.
"It's not enough. The manager might be in a position where he might even feel he has to step to one side.
"Serious questions really need to be asked. It's as bad as I've seen it. I know change was needed, Wenger was at the football club just a little bit too long.
"Now it looks as if the club has gone in a different direction. We're going only one way at the moment. This is relegation form.
"Do the club really realise how trying this is now going to be? Football people at the top of the club, make the decisions that need to be made. Otherwise Arsenal are going to plunge even further down the table."
Keown said: "It's a sad day. We don't say these things lightly because we still love the club. The club will never be taken away from former players.
"You have your view. They do their talking with their management and what they do on the pitch, we do that as pundits.
"I feel it's very sad. There were hardly any fans there tonight. They're voting with their feet. They knew what was coming there.
"Where's the desire, where's the identity of the football club. It was there under Wenger and it's ebbed away far too quickly. We've got to get it back."