Check in the preferences if you denied saving passwords in the past for the website. Go to Safari Preferences (
,), passwords tab. Unlock it and sort the list by passwords column. If the site shows "Never Saved", site will not prompt for saving credentials. One can also search for the site using the search bar in this password window.
Otherwise, manually adding the credentials is the way to go. In the same place, use add button and fill in the site URL and the password. Even then, some sites may not support autofill partially or even fully. It's upto the web developer. See if this site works that way or not after manual addition.
Safari may be unable to tell which fields are for username and password, credit card number and expiry date, and so forth.