Hmmm -- I think you mean you want to skip the code in the loop after the get fails and "get" the next file instead? I suppose you could use an inclusive "if", but the simplest way is probably with "next":

while($urllist =~ m{(http://.+\.html)}g){
 my $url=$1;
 my $html = get("$url");
 unless ($html) {
   print "Couldn't fetch $url.";
   next;
 }

 while($html=~ m{(find whatever I want)}gi){
  $mysearch=$1;
  print output "$url|$mysearch\n";}
 }
}
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"next" just means to move on to the next iteration of the loop, skipping any subsequent code.