Vanish and a pressure washer.
Seriously, without an extraction machine you're going to be a bit limited. The first thing I'd do would be to give it a really good rinsing through with just plain cold water - a job you could do less effectively in 2 hours using a sponge than a machine could do in 30 seconds.
Regardless of any machine or product though, if it's really bad this may be impossible to get out.
Best case scenario would be if it was a 100% polypropylene or nylon carpet and the spillage had been blotted out and then diluted down with water immediately as it happened.
Worst case scenario would be if it was a 100% wool carpet and it just had loads of vanish or 1001 splattered straight over it.
Probably a job for your local friendly carpet cleaner, or ultimately an insurance claim.