Another way to list all the files in a directory is with glob. It might be a good idea to filter that list so that only regular files are taken.

my @files = grep { -f } glob '/path/to/files/*';

for my $file (@files) {
    my $output = `/path/to/parser.exe $file`;
    # do stuff with $output
}
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Is your problem as simple as calling backticks in void context, without collecting the result?

System programs can also be launched with system, open, or fork-exec. Which you choose depends on what you want to do with them.