The only thing I'd have done differently is, rinse the entire carpet with plain hot water, but that does take twice as long. That's why I like to pre spray the carpet with cleaning solution and extract with hot water. Residual soap in the carpet can attract dirt.
I hate to say it, having worked in the business, but most people, like Pablos said, if you take the time and do it slowly and thoroughly, can achieve results similar to a professional. You can do a better job if the professional goes quickly and doesn't dry stroke to suck up as much water as possible. A thorough carpet cleaning takes 3 times the physical effort as a crummy job.