I doubt that it's possible to get carpet really clean without adding a significant amount of water, but it's important to suck it back out before more gets soaked than you want. In my past carpet cleaning experiences (at home or in cars - our Boler
has no carpet) I found that a surprising amount of vacuuming is needed to get the dirty water out - one pass certainly won't do it.
"Steam" cleaning is normally spraying hot water, possibly scrubbing with some kind of power brush, and vacuuming. That's what the rental machines and most home machines do. I'm not sure I would really use steam on a carpet.
If leaving residue is a concern, then why not do a final pass with just hot water in the machine?