I don't know about SQLite specifically, but not every DBD driver supports compound statements like that.

The portable way to do transactions with DBI is by using begin_work, and commit/rollback.

Usually you'd wrap the transaction in an eval to catch errors, so the following would be the more common idiom (copied from the Transactions section in the DBI docs):

$dbh->begin_work;

eval {
      local $dbh->{RaiseError} = 1;
      foo(...)        # do lots of work here
      bar(...)        # including inserts
      baz(...)        # and updates
      $dbh->commit;   # commit the changes if we get this far
};
if ($@) {
      warn "Transaction aborted because $@";

      # now rollback to undo the incomplete changes
      # but do it in an eval{} as it may also fail
      eval { $dbh->rollback };

      # add other application on-error-clean-up code here
}
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Update: Added RaiseError code per runrig's comment.