It's going to be darn hard to "de-focus" too much using a digital camera while keeping the main subject in sharp focus. The smaller the sensor, the greater depth of field you will have. Generally speaking, the smaller the camera, the smaller the sensor. Your Z740 has the smaller of the two more common sensors out there - 1/2.5". Most of the pictures you take with your camera are quite sharp from near to far distances and there is a reason for that which I will explain.
While we speak in terms of the 35 mm equivalency of digital lenses, don't forget that the digital sensors are usually smaller than a full-format 35 mm frame. Most of the more popular point and shoot cameras have the smaller sensors. It's only about 5 mm wide and 4 mm high. The lens on required to cover that angle of view on your camera is an ACTUAL 6-63 mm zoom lens. At these focal lengths, the background is going to almost always be in pretty sharp focus.
In other words, if you WANT to defocus the background, you are going to have to work pretty hard at it. You would have to zoom to the longer end of the lens and set the aperture open as wide as it will go, if your camera even allows you to control the aperture, and get pretty close to your main subject while having the background a fair distance away.
The bigger the sensor, the easier it will be to achieve pleasing bokeh. This means moving to a dSLR, which all have sensors about 20 times bigger than the typical P&S digicam. If you want to really go for brokeh (very bad pun intended), you can get a Canon 5D and you will get exactly the same effect you are accustomed to in a 35 mm camera, since the sensor is the same size as 35 mm film.
You can see some example of what is rather easily attainable with a DSLR at http//www.flickr.com/photos/samfeinstein/tags/bokeh/ Read the captions, though, because a couple of these are done with point and shoot cameras. Study the set-up to see how I did this. It's only doing exactly as I said in my answer above. If you like this effect, I agree with Anotoni that you are probably ready to move up to an SLR.
Wikipedia does pretty well on the subject of depth of field. See http//en.wikipedia.org/wiki/Depth_of_field
See also http//www.photo.net/learn/optics/dofdigital/