I have generated the EPS files my self. In the EPS files, I have set the \interpolate false option. I include them in the LaTeX source with includegraphics within TikZ (because I want several of them positioned nicely close to each other.)
Then I run the standard set of steps:
latex src.tex
dvips -Ppdf src.dvi
ps2pdf src.ps
In a text editor, I see that the PostScript source file, has preserved the full EPS file text. Even my comments in it (as it should). So the \interpolate false line has also remained. When I open the PostScript source with Evince (the GNOME pdf viewer), indeed there is no interpolation. Just for a check, with the editor I set \interpolate true and re-opened the PostScript file and confirmed that indeed now Evince interpolates the image. This shows that atleast Evince understands this option.
But when I open the src.pdf file that was output from ps2pdf. I see that the output is interpolated (anti-aliased) in any case! I also opened the PDF file with a text editor and found that only the most basic parameters of the EPS image have remained (like width or height). \interpolate false had been removed.
From the results above, I see that the problem is not in includegraphics or any of the LaTeX steps or even my pdf viewer. It is in ps2pdf.
In its documentation, it seems to have AntiAliasColorImages, AntiAliasGrayImages and AntiAliasMonoImages, but then in the following it says:
(note 0) This parameter can be set and queried, but currently has no effect.
So when I run the following command, there is no difference:
ps2pdf -dAntiAliasGrayImages=false -dAntiAliasMonoImages=false src.ps
I wanted to see if there is any way I can solve the issue. It is very important for me that anti-aliasing does not occur in the PDF file.

ps2pdfis part of ghostscript. Basically, it sounds in any case as though this is just a known limitation of the software. You could file a feature request, but I can't think of much else you can do unless you want to work on a patch yourself. – cfr Apr 26 '15 at 04:04/interpolate falseline in the PDF file might fix the problem. So I asked this question in stackoverflow: http://stackoverflow.com/questions/29873726/edit-non-binary-strings-in-a-binary-file . I will also try to contact the Ghostscript maintainers and suggest a feature request. – makhlaghi Apr 26 '15 at 04:29