If you don't need to know where on what line in file2 a line from file1 was used, then I would use something like this:

open (F1, "<file1.txt");
open (F2, "<file2.txt");
my $file2;
{
  local $/;
  $file2 = <F2>;
}

while (<F1>) {
  print "Line $. not found.", unless ($file2 =~ /^$_/m);
}
close (F1);
close (F2);
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This will put all the content of file2 in a simple scalar, and then check if the line occures by using a regex.