Out of contract at the end of the season, Ramsey is set to sign a five-year deal with Juve that will see him move to Turin at the end of the season on a free transfer.
And Keown is certain that Arsenal will miss the midfielder when he completes the deal.
“It’s the saddest thing of all really, how well he executed the plan today but in possession and out of possession,” the former defender told BT Sport.
“He’s obviously doing that to such an extent that [Mesut] Ozil can’t get near the team.
“But Ramsey’s not going to be part of their future and I find that sad.
“I find it a little bit sickening that he’s going to be leaving, they’re trying to make progress and one player who was singly so important won’t be a part of Arsenal’s future.”
Keown believes that Juventus' gain is undoubtedly Arsenal's loss, and questioned the logic of not fighting harder to convince Ramsey to sign a new deal.
“It’s madness and he’s going to Turin and Italy next season,” Keown added.
“It’s not as if he’s going to some Mickey Mouse team, he’s going to one of the best teams in Europe.
“Arsenal have lost him and I don’t know who’s making those decisions.”
The win over Chelsea left Arsenal just three points back of the Blues in the chase for the final Champions League place.