I'm primarily a newb with QTP, but given that it uses VBScript for its engine, you might consider doing a Google of "VBScript email" and you'll find a number of hits for using CDONTS(obsolete) and CDOSYS.
Now, these are primarily for Classic ASP for use in sending webmail, but I don't see why, conceptually, you couldn't use the same approach in your scripting to send simple pop3 mail.
I am not sure if you know this feature of QC or not:
when running a QTP test from the test-set of QC, in the 'Test set properties', there is an option to notify about completion of the test-set thru email, wherein you can set a message to be sent and the email addresses to which the email should be sent.
However, if the message that you want to send has some customized variables/parameters that can be captured only from QTP script and not possible to get it customized from QC, then as DJGary suggested, use CDONTS/CDOSYS.