It's not necessarily the lens that affects the DOF (depth of field)...but the aperture that the lens is set to.
Also, the distance from the camera to the subject and the subject to the background...will also be a factor in just how out of focus it looks.
Use your 60mm lens, put the camera into Av (aperture priority mode) and start shooting. Take one shot at the max aperture (F2.8). Then stop down the aperture and shoot again (higher F number). Keep doing this.
By the time you get to F11 or F16...it's likely that the flowers and the background will both be in focus...so the shot you want it probably in between.
Also, I think your camera may have a DOF preview button. You can press this button and the lens will stop down to the set aperture (otherwise, it's always at max until you press the shutter release). When you press the DOF button, the lens stops down (if you have it set smaller than max) and the viewfinder will get darker (less light coming in)...but, the DOF will also change. It might be hard to see at first...but if you look close...you should be able to see that more of the image will be in focus with a smaller aperture.
So you don't really need to take multiple shots, you could just preview it. But with digital (and the small viewfinders on these cameras) it's just easier to take multiple shots.