If you have a scrap of that carpet, stain it with the same ink and then clean it in the same way as you did the carpet that got stained. Let it sit for a few days for the dye to set. Then try a 1:20 dilution of household bleach in water. The bleach will remove the ink stain, but this test is to see how much of the original carpet color also gets removed (some carpets have pigmented colors, buy most are dyed). You will have to use lots of water to remove the bleach when you are done to stop the "cleaning" action.
Just get a swatch of fine art cotton fiber canvas, photograph a clean section of the carpet, print it on the swatch and mount it over the offending area!!! No bleaching, scrubbing or explosions (unless from wife)-and probably not much 'photoshopping' required. Don't sweat it.
Having had this happen to me, with a dye based canon ink, I would say get the water as hot as possible, I use a little green machine and a steam buggy to clean with pretty good results.