Is there a way to update CiviCRM through the Drupal Admin/Modules panel?
I feel your pain.

There is no way to do it through the modules panel.

However, I believe the instructions you are following are unnecessarily complex. What we do is back up, then delete the civicrm directory, upload the new version and then run the update script. We don't bother disabling and enabling extensions. We use maintenance mode if it's during working time - you don't need to unless you expect people to try and use the system during the upgrade. 

To be fair we do have a test system that we do it on first. But we have not had any trouble (sometimes things don't work after upgrade but this has always turned out to be the result of bugs rather than anything we did), and in any case you are already backing up first so if something did go wrong you could restore.

I think this is quite a common approach, see for example https://civicrm.stackexchange.com/a/11436/465

As for the error that you say appears after upgrade - usually one or two clears of the drupal cache will fix such things http://www.inmotionhosting.com/support/edu/drupal-7/configure-caching/clear-caching