On November 18, 1948, the Norwegian Nobel Committee decided to make no award that year on the grounds that "there was no suitable living candidate". Chairman Gunnar Jahn wrote in his diary: "To me it seems beyond doubt that a posthumous award would be contrary to the intentions of the testator."
So basically they were going to give him the award but they decided that Nobel wouldn't have approved of giving the award to someone already dead so instead they gave it to no-one that year. Can't really say I see the logic. It would have seemed better to have awarded the prize money to a charity in his honour or some such rather than just not awarding it at all.
Does raise the interesting point though that there was obviously precedent for not awarding a Nobel prize in a given year due to a lack of any candidates standing out. Could have done that instead of awarding it to Obama but as I said, in so far as I can see I'd rather someone gets the prize money and puts it to good use than not award the prize at all.
Do I think he deserved the prize? I imagine there are those more deserving. Does it particularly bother me? I read he was giving the money away to charity, so not really.