The claim “markets are inefficient” can imply at least two things:
1. The job of allocating capital to investment projects will be badly done by markets.
2. It’s possible for an individual to out-perform stock markets without taking on extra risk, by spotting under-priced assets.
This reminded me straight away of this paper (PDF) by Alfred Rappaport which is worth a read, even though I'm not 100% convinced by it any more. Rappaport basically says that 1 can be true, even if 2 is not. Markets can be informationally efficient (available information is immediately factored into the price) but allocatively inefficient (because the info is duff/irrelevant, investors are biased etc). So you can't beat the market, but the market can still be off-target. Which is a neat way of explaining things, but (I argued previously) perhaps doesn't tell us all that much.