As far as I'm aware, it is ok to use BSD licensed source code in a closed source application for commercial purposes, but do you have to reference the BSD licensed code at all? In other words, do you have to make people aware in the EULA that the software contains parts of BSD licensed code?
There are various forms of the BSD license, the "four clause", the "three clause", the "two clause" and the "zero clause", and they all contain different restrictions.
The "four clause", the "three clause" and the "two clause" all contain the following text:
Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
This would indicate that the answer to your question of "do you have to reference the BSD licensed code at all" is not specifically the code itself, but you do have to reproduce the original copyright notice and the BSD license text.
The answer to your follow on question and whether it needs to be mentioned within the EULA is entirely depends what the license text means by "other materials provided with the distribution". If you do not include the copyright notice and BSD license within the documentation, then I would include it as part of the EULA. Either would seem to satisfy this clause.