I know exactly what you mean (I use Pipedrive as well). Unfortunately, it’s not quite as good with Asana. You have to forward emails to email@example.com to turn emails into tasks. You can also forward tasks to a specific project or conversation thread.
Some client’s I’ve worked with auto-forward emails to specific projects e.g. if they have a client project, all emails from the client are auto-forwarded here.
You can read more about creating tasks from email here.
If you have any more questions or need help with Asana set up and training, please feel free to book a free 30-minute introductory call with me to discuss my Asana consulting options.