Here is yet another method, based on Regexp::Common:

use strict;
use warnings;
use Regexp::Common qw/comment/; # <== 

my $html = <<'END_HTML';
<p><b>Hello World</b>
<!-- This comment would need to be removed from the entry -->
</p><font color=red>It is Sunday!</font>
<!-- also this--><p>this should stay
here</p><!--this should go-->
END_HTML

$html =~ s/$RE{comment}{HTML}//g;  # <==

print "$html\n";
[download]

Result:

<p><b>Hello World</b>

</p><font color=red>It is Sunday!</font>
<p>this should stay
here</p>
[download]