WordPress creates a .maintenance file during the update process which indicates that your site is in the maintenance mode. Unless this file is removed your site will remain in the maintenance mode and your users will continue to see the notification.
Once you have updated WordPress, all you have to do is delete .maintenance file from your site’s root folder using FTP.
If you can not see .maintenance file in your site’s root directory, then make sure you checked your FTP client to show hidden files. In Filezilla, you can force it to show hidden files by clicking on Server » Force showing hidden files from the menu bar.