My application logs properly to some log file, but I'd enjoy having use of these logs within the database too. I attempted django-log-db but it is not suitable for Django 1.3. Sentry is overkill since it requires implementing a Sentry server.

It is possible to simple Django solution for logging towards the database?

You should use python logging module with django.db.backends and custom handler that saves massages to database. However I highly recommend you to employ sentry, you are able to configure it within your django project so you don't have to run it as being another server. It aggregates all messages and causes it to be super easy to evaluate.