First thing you need to do, is prime that repair area.... if you don't, it will end up a different color.
Ive had a LOT of practice with MANY different textures, on walls and ceilings. Your best helps here, are patience, persistence, and a willingness to do it over if doesnt look quite right, hehehe. An artistic 'bent' helps too.
For a small knockdown finish, there are a couple of good ways to apply the texture, in small areas, without a compressor.
1) paint brush! -- only don't use it to 'paint'. Instead, use the very tips of the brush to 'stipple' the texture on. Another method is to "fling" the texture onto the wall, with the brush.
2)Sponge -- you can use a rough sponge to apply texture... do not slide the sponge... dab it, reloading it often, but not too heavily
3)Crumpled plastic bag (the bag a loaf of bread comes in works great) -- same method as with the sponge.... adjusting how 'tightly' you have the bag crumpled will affect how the texture looks when it is applied.
Now.... after getting the texture on the wall.... you need to "knock" it down.... this is accomplished by taking a drywall taping knife, or wide putty knife, and slimply dragging it down the wall. (I say 'down' becuase that is the direction most knockdown wall texture is done.... look closely at your own texture, with a couple of swipes, you can tell pretty quickly if yours is the typical downstroke, or something else.)
Now... a couple of things to consider when you do this... and these things will affect the outcome of the texture.... First... How 'heavy' is the texture you are applying? You can make it more solid, and dry, or, by using a wetter compound, you can make it somewhat thinner, or sparse.
Second ... the amount of time between when you apply the texture, and when you use the knife to knock it down. Knocking down texture when it is first applied, will look different from letting it set a few minutes, before dragging tha knife across it.
If I were to walk into your home, I could figure out which approach to use, in a matter of minutes...because Ive done so many of them, hehehe... Practice Practice Practice.
You can attempt your texture match on the first try.... but dont be discouraged, if you need to scrape it off and try again, to get it 'just right'. Or, you can use some scrap cardboard, and practice on a few pieces altering things as Ive mentioned above, to get different results, and see which matches your wall finish the closest.
I have used these kinds of approaches to match perfectly, repairs as large as 3 ft square....if your repair is larger than that, then you may want to seriously consider renting a compressor and hopper gun. If you rent a hopper gun, then tape some plastic to the walls... and fire some practice shots on them, hehehe.
Feel free to email me, if you need more detailed advice.
Have Fun!