No. Although FTP and HTTP support some form of authentication, the TFTP protocol does not. As a result, to avoid a false sense of security, we've decided to omit this feature entirely.
Trivial was designed to make it quick and painless to set up a TFTP, FTP, or HTTP server to transfer files to and from network equipment without having to install system processes or worry about configuration and security. With Trivial, there is no risk of inadvertently sharing anything other than what you've explicitly dragged into the list of shared files, regardless of the sharing protocol used. The Trivial server process strictly validates all requests and operates within a strict sandbox that prohibits it from accessing anything else on your file system.
Trivial does provide a simple set of access controls that apply uniformly across all protocols. See How do the client access control options work? for more.