In addition to "tell them that you cannot fix bugs that aren't reported" (as covered in recent answers) you need to make reporting a bug as easy as possible. Most non-IT people feel intimidated by the prospect of having to use the ticket system and think it's far too complicated for something they can simply tell someone.
If a colleague starts ranting, show them the ticket system (where to find it) and file the bug together to show them how to do it. If possible, create a template with the most important information you need:
- Name of the app (you won't believe how many people forget that)
- What did they want to do
- What/where did they klickclick
- What happened instead of the desired behavior (the actual bug)
- Add a screenshot if possible
- Name of the bug reporter for call back
In addition, encourage colleagues to report bugs. Make it clear to them that reporting a bug is good, helpfull and has a positive outcome. Some might feel like betraying you by revealing "mistakes" you made.