There's a number of ways of doing this - none of them will be as good as actually shooting with a wide aperture but you can do better than using a quick selection..

Thing to remember is, there's not just 2 planes of focus in your shot - you gradually go from focus to out of focus - just bluring the shot and then putting a cut out of the focused bit in will look like, as you say, cardboard cut outs.

Try this - open your photo in photoshop - duplicate the layer. Apply a blur (try lens blur although gaussian should be ok - or maybe smart blur.. pick whichever works for you).

Then apply a layer mask to the blurred layer.

Then, with your brush set to paint black and opacity about 5%, gradually paint over the bits you want in focus. It will take a while but you want to achieve that look like the focus fades out - not just with harsh lines.

You can also look into advanced use of lens blur filter but that's a bigger topic.

Try the method I mentioned and post your results here - I'm sure someone will (eventually) offer some more advice for you.