The simplest Perl solution I can think of is

perl -MIPC::System::Simple=system -nle'system p4 => delete => $_' dele
+tefiles.txt
[download]

IPC::System::Simple does error checking for you.

Update: Shorter, but the error messages are a little weird:

perl -Mautodie=system -nle'system p4 => delete => $_' deletefiles.txt
[download]