No that size tip should be able to get a pretty thin line, something in the range of a pencil line. I use a.35, a little bigger, and it's very rare that I wish for more. What paints are you using? and what pressure? Both can make it harder for you to get what you want.
You should be able to get finer lines a few ways with what you have. Moving a bit faster, getting closer, lowering your air pressure and thinning your paints, are the main ones I tend to use.
Lowering your air pressure helps a lot, and it's the easiest thing and can make a big difference. Some painters keep theirs down as low as 5 or 10 psi, too low for me but everyone kinda has to find their own balance for what they are doing. T shirt guys can run 40-50 psi with textile paints (I've heard), again not for me, but it shows that each application has different set-ups.
Over-reducing your paints can make a huge difference as well. Straight paint out of the bottle will almost never make as thin of a line as something more "watered down". Try reducing your paints a little bit at a time and do some test sprays, and try a little more each time until it get's closer to what you are looking for, or until it's so thinned out that it "skates" which is when you make spiders and caterpillars,
.
Now you've found "too far"... keep track of the drops of paint compared to drops of reducer and you'll have a rough idea where the edge of where you can go is. Everyone finds what works for them for each application.
Another thing is you can remove the needle cap that protects the tip of the needle, this will allow you to get closer to your work, and the air flows smoother without the cap. Be
careful though, you can easily damage your needle by bumping into something, dropping it, or even hitting your paint surface. I've folded over a needle this way, painful lesson. I was without an airbrush until I could get a new needle and nozzle set. Put the cap back on after you're done doing your detail work, a trip on a air hose could ruin your day.(I've done that as well... and dropped one.)
So again it's all a balance between speed, distance, reduction, and air pressure. Try changing one thing at a time though, or you'll never know which part works for you and which didn't. Keep track of what you changed and the results it gave. I like to do a repeating pattern as I go, and write next to each one what psi, and reduction I used.
Sorry this got so long,
. I looked up and I'd written more than I thought.