Since you are on Windows you will need to binmode() your output handle. If you don't it will automaticly add the CR to your LF every time you output a LF.

open(INFILE, "< input.txt") or die "Failed to open input: $!\n";
open(OUTFILE, "> output.txt") or die "Failed to open output: $!\n";
binmode(OUTFILE);
while (<INFILE>) { print OUTFILE }
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This code will remove the \r at the end of the line only. If you want to strip all \r's you will need to do s/\r//; imediatly prior to the print statment.