If your file is simply tab-delimited, you can add the file column without using any external modules, simply adding tab and filename at the end of each line :) Like this:

{
local @ARGV = @FILES;
local $^I = '.orig';
my %seen;
while (<>) {
    (s/$/\tFilename/, (print), next) unless $seen{$ARGV}++;
    s/$/\t$ARGV/;
    print;
}
}
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This fragment of code also saves all original files with '.orig' extension.