I found that there is a warning on my site saying that manual updates of Drupal core is required.
How can I do it safely?
See this article from the Drupal.org documentation under section "MINOR VERSION UPDATES".
In short :
Since you haven't replaced the files-directory, all basic settings (settings.php) there should be ok.
That's the main principle in a minor update. Of course you always should take precautions like backups, and take care of all files outside the sites directory that might have changed.
For more info see : see http://drupal.org/node/1223018