The Gunners went into the Europa League last-16 clash as the underdogs against the Italians, who were unbeaten in their last 13.
Keown told BT Sport: "They picked themselves off the canvas, there is no doubt about that.
"They were in somewhat of a hole coming into this, everyone talking about not if but when Arsene Wenger was going to walk away from his job and this is the first step back.
"They were competitive, like street fighters, more at boiling point. It was almost as if people were able to walk all over them but not tonight, and that's the very first step."