The north London club spent nearly £70million in the summer and Keown thinks the Arsenal boss needs more.
Keown told BT Sport: "Performance is completely different from that defeat at West Ham. That manager is worth his weight in gold. Got to get behind him.
"We don't know what's happening internally. But they can look at recent signings and see they're all making a difference.
"He has spent money wisely, give him more money to spend! I don't expect him to this window but I do in the summer."