Usually you can widen the DOF by using a smaller aperture (high f-stop number).
That makes the background more in focus, and usually it makes for an overall sharper picture. However, most people don't use crops, so sharpness isn't an issue when resized for the web.
But you already shot the photos at f/20 and f/13, so that's pretty narrow.
You can up to the ISO (probably to 400 or 800) and still get decent shots. That way you can use a wider aperture (smaller f-stop) and faster shutter speeds. With practice, you can then eliminate the need for a tripod (although they are still very useful).
Also your lens.. the Micro Nikkor 60mm f/2.8 is sharpest at f/5.6 and f/8. I would suggest trying some shots at a wider aperture like f/2.8 and f/4 and see if you like it. They make for a dreamier background too (as well as faster shutter speed like I mentioned).