DirectAdmin doesn't have such a feature as what cPanel does.
However; there has been a request for something similar:
https://forum.directadmin.com/showthread.php?t=58773
The method DirectAdmin uses is as follows:
Admin
-> Log Viewer
-> selecting Exim Mainlog
-> use grep to find what you want.
This is essentially how we search for mail on the server at command-line (SSH) they just have interfaced this into the panel to make it a little easier.
Unfortunately, the downside to this is that in order to read the log properly -- you need to be somewhat familiar with how Exim handles its output for incoming/outgoing mail.
cPanel just makes the process entirely user-friendly by formatting the data for easy-to-read use; but uses the same data differently.