Unless you can receive or create a task and then immediately complete it, you will need a task management system.
This could be as simple as writing down tasks on post-it notes or as complex as recording the task in a system such as Todoist or Trello and utilising the full range of available features.
No matter the system you use, consistency is key to making it work.
If I receive tasks and write some down, create Trello cards for others, and make a mental note of (i.e. risk forgetting) others, then I’m bound to lose things.
If tasks emerged only through one source – email, for example – then it could be feasible to go back and review periodically to ensure that nothing has been missed. But tasks typically emerge from myriad sources, making the process of reviewing the sources later ungainly at best and unfeasible at worst.
Thus, consistency is key.
I would advise you to pick your system, and stick with it.