The Swedish minnows picked up a famous win at the Emirates Stadium, but could not prevent the hosts from advancing into the round of 16 courtesy of a 4-2 aggregate success.
Keown has claimed that a number of Arsenal's fringe players failed to perform, although the former defender specifically had a swipe at Nigerian attacker Alex Iwobi when discussing the shock result in London.
"It is not a tap you can turn on and off if you are going to perform," Keown told BT Sport. "There are so many players on the pitch there, they get limited opportunities and it is worrying that they are not at the same level.
"It reflects on the training and how they are prepared mentally and physically. It was an embarrassing first-half performance. Arsene Wenger is in the mood for change and if you look at the players he has got rid of in the last two transfer windows, it is staggering.
"And there might be one or two more that aren't good enough and are now fighting for their future. Whenever you play, you have to make your mark and they weren't at it.
"I'm looking at Iwobi, wondering what direction his career is going in. He is getting so many opportunities but there is a list of there tonight that won't be happy with their performance."
Arsenal will take on Italian giants AC Milan in the last-16 stage of the Europa League.