Despite taking an early lead in the tie through Alex Iwobi, the Gunners found themselves 2-1 down just after the hour mark before a late Ismaila Sarr header completed a huge win for the hosts.
Arsenal seemed to crumble after Sokratis was dismissed for a second bookable offence 41 minutes into the contest, with a superb Benjamin Bourigeaud strike and an own goal from Nacho Monreal turning the tide in Rennes' favour.
Despite facing a deficit, Emery elected to take off star striker Pierre Emerick Aubameyang in the second half and Keown admitted he was puzzled by the 47-year-old's tactics post-match.
"It was a total disappointment," Keown began - as per the Daily Mirror. "Arsenal were ill-disciplined and it's cost them. There were several decisions for the manager to make and he got them all wrong really.
"There was a real lack of urgency and that ill-discipline has really cost Arsenal tonight.
"I know Emery has got an incredible record in this competition and it's not over yet but they are going to have to show some real spirit and they really did make it hard for themselves.
"It seemed to me that the decisions Emery made just didn't work. I don't know why he took off Aubameyang and tried to play without a striker. As the team with 10 men, I thought he would be the man you would want to have on the counter.
"The ill-discipline seems to be creeping into the team and it needs to be sorted. It's costing them at the moment."
The Gunners now have a mountain to climb at Emirates Stadium for the return leg next Thursday, but before
The Red Devils will arrive in north London on Sunday in search of a tenth successive away win under caretaker boss Ole Gunnar Solskjaer, with both teams vying for a spot in the Premier League's top four.
Ahead of the clash, Keown revealed he is hopeful Arsenal can upset the odds and secure a vital win - but only if Emery fields his strongest possible starting XI.
"At the moment the away form has been a bit of a disaster for Arsenal," he added. "They have been inconsistent but their next game is at home and they have been strong there.
"I think Manchester United could be the perfect team to play next for Arsenal and it could be season-defining if they win and I think the fans will demand it so bring them on.
"I think the problem Emery is having is he is not picking his best team. You have to pick your best team, I know Aaron Ramsey is leaving but if you have to play him so be it."