Did you actually get a "failure" notice or error message? Or did it complete but now you cannot get in?
Those are two different scenarios and could be caused by different things - an update that completes fine but then leaves you unable to login *could* be caused by a Plugin or Theme conflict....if you have FTP access you can try renaming your Plugins folder first, and renaming the folder of the Theme you were using to force WP back to the default Theme.
If it simply failed and gave you a failure/error message, well sometimes the automatic updater fails....we all wish it wouldn't, but it does.
Again, assuming you have FTP access to your site, I would recommend trying a manual update, it's not difficult.
http://codex.wordpress.org/Updating_WordPress#Manual_Update
Just be sure to backup your database if you can using phpMyAdmin first, and don't overwrite your /wp-content/ folder, as that is where your Themes and Plugins are.
When I do a manual update, I download the latest version of WP, unzip it, and simply delete the /wp-content/ folder that it comes with, then upload all the rest. If you're very brave and are careful, you can be sure you won't leave detritus from the old version by first deleting all the files and folder in your WP folder EXCEPT the wp-content folder and your wp-config. file
ALWAYS backup everything first, but this should get you back in.
