Shoot festival concerts during daylight hours. Honestly, that's about it.

Theatrical/concert photography is about the most challenging there is, both in terms of pushing the equipment you use to the absolute edge of their capabilities and in terms of requiring every bit of skill and experience you might have as the photographer.

Photography is the art of capturing light. Most concerts don't offer much light to capture and what light there is to capture is changing rapidly and the subjects are usually very animated. So the traditional solution to not much light (longer shutter speed using a tripod to hold the camera still) doesn't work because nobody on stage stands still for 10-15 seconds while you take a picture. The traditional solution to capturing motion (faster shutter speeds) doesn't usually work because there isn't enough light to capture a good image on a small sensor with a narrow aperture. In the end you have to balance the two as best you can AND use gear that allows you to capture as much of the scarce light that is present in the scene in as fast a time as possible. That means fast lenses (wide apertures), larger sensors, and cameras that are highly responsive (fast handling). Most point-and-shoot cameras trade all of that away to make them compact, light, and relatively inexpensive.

Your Panasonic Lumix DMSC-TZ10 has a sensor that is about 1/16 the size of a "Full Frame" sensor. That's roughly 4 stops of light difference in terms of light gathering capability. The maximum aperture of f/3.3-4.9 is anywhere from 1/3 to 1 2/3 stops slower than an f/2.8 lens, and 2 1/3 to 3 2/3 stops slower than an f/1.4 prime lens! So at a middle focal length where your camera is at f/4 you must use a shutter speed 32X slower than a FF camera with an f/2.8 lens! If the pro camera can get the shot at 1/320 second (where it is about 50/50 chance you can freeze the motion of the performers if you time it just right), your point-and-shoot needs 1/10 second to collect the same amount of light. Assuming your camera didn't move at all in that 1/10 second (near impossible at a concert, even your tripod will vibrate with the energy pumping out of the speakers) everything on stage is still going to be a blurry mess for all but the most static of performers.