Please do not use this word.
While Webster 1913 may give the word "administrate" some semblance of authenticity, it still strikes many people as a jarring and unnecessary buzzwordification of the word "administer". "Administer" is a verb; an "administrator" is a person who administers something; "administrate" is -- or at least appears to be -- a back-formation from "administrator".
Using this word is like writing "utilize" instead of the simple verb "use", or "proactive" instead of "active" as an antonym for "passive".