In modern Perls -- I'm not sure which versions qualify here, maybe 5.6+ -- Perl will check whether the contents of the variable has changed. If the content of the variable has not changed, the regexp is not recompiled.

For example, compare

my @words = (
   'foo',
   'bar',
);

foreach (@array) {
   foreach my $word (@words) {
      if (/\Q$word/) {  # BAD!! $word always changes.
         print;
         last;
      }
   }
}
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to

my @words = (
   'foo',
   'bar',
);

foreach my $word (@words) {
   foreach (@array) {
      if (/\Q$word/) {  # GOOD!! regexp only recompiled when needed.
         print;
         last;
      }
   }
}
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It's not always practical to change the order of the loops. For example, when one of them reads from a file. In that case, the solution is to precompile the regexps. For example, compare

my @words = (
   'foo',
   'bar',
);

while (<FILE>) {
   foreach my $word (@words) {
      if (/\Q$word/) {  # BAD!! $word always changes.
         print;
         last;
      }
   }
}
[download]

to

my @words = (
   'foo',
   'bar',
);

# Precompile the regexps.
my @regexps = map { qr/\Q$_/ } @words;

while (<FILE>) {
   foreach my $regexp (@regexps) {
      if (/$regexps/) {     # GOOD!! $regexp is a compiled regexp.
     #if ($_ =~ $regexp) {  # GOOD!! Alternate syntax.
         print;
         last;
      }
   }
}
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If you're trying to match constant strings rather than regexps, then I recommend Regexp::List:

use Regexp::List ();

my @words = (
   'foo',
   'bar',
);

my $regexp = Regexp::List->new()->list2re(@words);

while (<FILE>) {
   print if /$regexp/;
  #print if $_ =~ $regexp;  # Alternate syntax.
}
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By the way,
for ($loop_index = 0; $loop_index < $#patterns; $loop_index++) {
is much less readable and no more efficient than
for my $loop_index (0..$#patterns) {
You could also have used
foreach (@patterns) {

Finally, in your case, I'd use

my @patterns = qw(
   create
   drop
   delete
   update
   insert
);

my $regexp;
$regexp = Regexp::List->new(modifiers => 'i')->list2re(@patterns);
$regexp = qr/\b(?:$regexp)\b/;

...

while ($data = $sth->fetchrow_arrayref()) {
   # index is faster than regexps on constant strings.
   next if index(lc($data->[10]), 'tempdb') >= 0;

   if ($data->[13] =~ $regexp) {
      print "$data->[3] $data->[9] $data->[10] $data->[13]\n";
      last;
   }
}
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Update: Bug Fix: Changed $word to $_ in map's code block.