When using rsyslogd you can create a filter rule that matches some vsftp log messages of interest and emails them to you. Rsyslog has an email output module.
Other syslog daemons may provide similar features.
Perhaps you also need to adjust some vsftpd options to get all events of interest reported.
In general, the question is, if you really want to get an email for each bad login attempt - because bots mechanically trying logins are nothing special (i.e. you would get spamed).
Another strategy is to use rsyslog to filter vsftp messages of interest to a separate log file and let a cron job notify you - say - every few hours - if the file has changed. Perhaps also mailing it as attachment if it is not too big.
Using rsyslog you can configure an appropriate log rotation period, too that matches your cron job call pattern.