Can you explain that in simpler terms?

Sure. This call:

my $auth = Mymodules::Auth->auth($username, $passwd);

is a method call. See any of the Perl documentation about OO for why this is. The important thing is that it passes three arguments. The first argument is the invocant, the string Mymodules::Auth.

The sub you're calling is not a method, in that it doesn't account for the possibility of an invocant.

sub auth {
   my $username = shift @_;
   my $passwd = shift @_;
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$username will end up containing Mymodules::Auth, $passwd will end up containing what you passed as the username, and the password will stick around in @_.

Instead, if you plan to call this as a class method, deal with the invocant:

sub auth
{
    my ($class, $username, $passwd) = @_;

    # ... more code here
}
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Still, I can't explain why this causes the error message you kinda sorta don't really quote. You'll have to post more code and the exact error message you receive; you know the drill.