The 2014 Corolla is a new design, likely to have some bugs in the first few model years, plus it is bigger, harder to park, has options some people don't want to have to pay for, and folks who buy used cars may be going after the current-design Corollas (2013 or older) while the getting is good, driving up the price. That might be one explanation.
Another might be that the ads you see in the newspaper quoting $15K for a new Corolla, well, believe it or not, it is possible it isn't actually possible to purchase one at that price. When you go, they'll say they only had one, and it is already sold. But they have another super-duper one with blue-tooth and a rear window defroster which is only $21,000.
Take a look at the Kelly Blue book used for used car values, it is usually fairly accurate. I think you can get this info on-line gratis these days.
One more idea, you might have better luck looking for a 3 or 4 year Corolla with 60,000 miles on it.