I'm afraid there's no magic, totally reliable way to do this.
All the vocal eliminators I know--including Audition's--work on the basis that lead vocals are usually panned centrally in a mix with instruments panned left and right. At the simplest, a vocal remover inverts on of the stereo tracks, hopefully causing the vocal to cancel itself out with other instruments remaining more or less intact. As you can see, this is fraught with risk--anything else in the centre channel will also be cancelled while parts of the voice that aren't central (stereo reverb for example) will remain.
Audition's "Centre Channel Extractor" on the Stereo Imagery menu is as good as any at trying to do this and better than most. All I can suggest is having a play with the settings (including the FFT size on the advanced menu) and get things as good as you can. However, I fear that the only way to get a totally clean instrumental version of anything is to either record it yourself or get access to the original multi track recordings from the record company.
Another way if you have Music Sequencer software is to see if there are any MIDI arrangements of the backing tracks available on line anywhere.
Or you could look for a karaoke version - though I suspect that the name of that Timberlake song is a misnomer
I just did a quick Google and there are several karaoke versions available. At least one of them didn't sound bad (if you like Timberlake).
Well, thanks for your help all. I'll just play around with my settings. If I get desperate enough, I'll get in touch with the recording company. As for karaoke versions, I have seen many of them and already looked into them, but none of them sound exactly like Justin's original song, which is a must for me.