(disclosure: card-carrying member of the SNP writing here)
As opposed to doing what?
Expecting the SNP, in particular, to renounce its core policy / wither up and die would be laughable.
The main reasons it's doing well, therefore "carrying on as if they won"? Pick any of the following:
45% loses a referendum, but in almost anything other than a pure two-party system, it landslides a first-past-the-post election - like the rest of the UK, the big thing in politics at the moment is the May general election which looks to be shaping up very well indeed for the SNP - some of the wilder polls predict a constituency map looking like Bart Simpson with a couple of plooks (spots, for the English-speakers) - i.e. most of Scotland going SNP (yellow) with two (red) bits holding out for Labour.
Speaking of Labour, its support appears to have withered spectacularly. Some of this is probably due to the referendum - Labour and the Tories shared a platform, and it should not be underestimated how much some voters in Scotland still hate the Tories. Considering it was the Labour areas that, on the whole, voted "Yes", it's not difficult to see how this political realignment happened. The Lib-Dems are still suffering from being in coalition with the Tories who will be lucky to keep their one Scottish seat.
However, the most sensible reason is probably that a large enough percentage of voters see Lib/Lab/Con as predominantly English parties, focussed (understandably, considering England's far greater population, number of seats, etc.) on delivering what English voters want with little regard for Scotland. The SNP can make a good case for being the only party that will try to get the best deal for Scotland in Westminster, especially if they become the third largest party and either Labour or the Conservatives are unable to govern alone or with the other parties. Lots of Scots find the idea of Ed or Dave being impotent unless conforming to Scottish interests extremely appealing. (Having said that, there is the nightmare option of a Labour/Conservative coalition...)