One way is to add some negative "kerning" between the quotation mark and the period:
\documentclass{article}
\begin{document}
Here is an unkerned quotation mark: ``\dots''.
Here is a kerned quotation mark: ``\dots''\kern-0.5em.
\end{document}

The TeX command \kern-0.5em inserts a negative space between the quotation mark and the following period. You will have to play a little with the exact spacing, but using a measure like -0.5em which will scale with the font size should work reasonably well.
Automatic Kerning with LuaLaTeX
As others have suggested, you can do this with macros, but if you want to do this automatically, you appear to need to include this kerning information in the font specific kerning table. This can be done with LuaLaTeX as follows:
First create a file: Palatino.fea
languagesystem DFLT dflt;
languagesystem latn dflt;
feature kern {
pos \quotedblright \period -1000;
} kern;
Now load this font information using fontspec:
\documentclass{article}
\usepackage{fontspec}
\setmainfont[FeatureFile=Palatino.fea]{Palatino}
\begin{document}
Here is an automatically kerned quotation mark: ``\dots''.
Here is a manually kerned quotation mark: ``\dots''\kern-0.5em.
\end{document}
Note that you need to compile this with lualatex now, and that you will need to add the custom kerning information for every font you would like to use.

\quo{…}that enquotes the content and does checks and behaves correctly depending on the last character. – Manuel Sep 23 '14 at 21:02