How to justify selection of existing algorithm for a new application area?
There is a pretty standard method in my area of research for design of experiments and I have discovered that one step could be automated to save time. The automation can be done with a variety of standard machine learning algorithms and I've selected one that:


It sounds like you are working out a problem in your field that has never before been addressed using machine learning algorithms, and you are the first to try this approach. 


  is used pretty often, according to literature
  provides very satisfactory results (high accuracy) on my data


The application of such machine learning algorithm has provided you good results, where I assume that good means at least good enough as the state-of-the-art in the field. 


  My question is, how could I rule out the alternatives or at least justify my choice (for example, in the "related work" section) against other algorithms that could possibly work better/be more suitable?


If my assumptions above are correct, then your paper's main contribution is to solve a known problem in a novel way. This is sufficiently good an achievement that does not need to be justified. It sounds like your only problem is to convince a community of academics that are not normally exposed to machine learning, that your choice is reasonable (NOT optimal) and your results robust. 

In machine learning - both in academia and in industry - you often find yourself 
using a model that is good enough: it does not have to be the best, nor the most complex; what has to do is do the job correctly and provide interesting results. All you have to do in your paper is then to explain the algorithm and show why the results are robust.