Can you tell us what you're getting, and what you're expecting? This seems to work fine for me...

while (my $line = <DATA>)
{
    chomp $line;
    if ($line =~ /(#include)( ")([^g]\w+)(\.)(\w+")/)
    {
        print "$. MATCH [$line]\n";
    }
    else
    {
        print "$. not match [$line]\n"
    }
}

__DATA__
not an include
#include "foo.h"
#include <foo.h>
#include "gfoo.h"
[download]

This produces:

1 not match [not an include]
2 MATCH [#include "foo.h"]
3 not match [#include <foo.h>]
4 not match [#include "gfoo.h"]
[download]