You can use anything to apply texture paste onto a canvas or sheet of paper. Different tools will produce different textures. A coarse or stiff-haired brush will create more marks in the paint than a soft brush. I like using a painting knife because it's easy to get the paste out of the tub, it's easy to spread out and to scratch patterns into the paste.
Spreading texture paste with a painting knife is akin to buttering a slice of bread with a springy knife. The action is the same, and if you don't like what you've done you can scrape it all up and start again.
In the photo I'm using texture paste straight from the container, without mixing any paint into it. This particular brand looks very white at this stage, but won't be when it's dry. You can also see that I've applied applying the paste on top of some dried paint -- as with all acrylic mediums, you can use it at any stage in a painting's development.
Next: creating texture by pressing a knife into the medium...