Would providing an explanation due to a high cost of an article and unavailability in the library be a good reason for exclusion criteria when working on a systematic review?
Yes, you can, try your best to get that article through your colleagues/friends in university settings. Still can't get it, Please exclude and move on.
The objective of a systematic review is to find and use ALL studies that address your research question. Short of that, you could be satisfied with a random sample of all studies. Exclusion of studies on the basis of criteria unrelated to the research question (e.g., cost of article, language the article is printed in) can result in a biased set of studies. Thus, in my opinion, exclusion of an article on the basis of cost is not acceptable. Seek out financial support from your research mentor, your department, etc.
The objective of a SR is to find and use all studies. Before exclude the article, you have to send an e-mail of the corresponding author (with high probability the answer will be positive)