As always, you will need newer graphics cards to take full advantage of newer games. That has always been true. Whether it is simply for technical reasons (newer cards have higher performance), sometimes there are specific graphics features that require newer cards.
Usually using an older previous-generation graphics card just stops you using some of the more clever effect, like a lot of particle physics that comes with current DX10 cards. But the games should almost always still work with slightly older cards (eg DX9 cards).
It's not as if suddenly from next-week onwards ALL games will FORCE you to have a DX11 card. Most people won't get a DX11 card for at least 18 months from now, probably a couple of years, but DX9 and DX10 cards should still work just fine until then.