tr doesn't do double quote interpolation, and this is documented. If you want it you've got to use eval:

my $count;
eval qq{ \$count = \$inp_row =~ tr/$de/$de/; };
die "Problem in eval'd tr: $@\n";
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Update: Bah, that wasn't directly to it. Direct link to the relevant section in perlop: tr///. Specifically you want the paragraph starting "Because the transliteration table is built at compile time . . .".