Corluka was one of several furious Croatian players who confronted Nishimura after he awarded a contentious penalty to Brazil in the tournament's Group A opener on Thursday (local time).
"We were quite simply shocked with the fact that he communicated with us in Japanese all the time," Corluka told Croatian media on Friday.
"It is just hard to fathom that an official who speaks no English or any other international language was allowed to be in charge of the World Cup's opening match."
Nishimura is a very experienced official and was the 2012 Asian referee of the year. He was also the fourth official at the 2010 World Cup final.
Two-goal Neymar converted the penalty to give Brazil a 2-1 lead midway through the second half and midfielder Oscar stabbed the third in added time moments after Croatia missed a good chance to equalise.
Brazil take on Mexico in Fortaleza on Tuesday while the Croatians play their next match in the hot and humid Amazon city of Manaus on Wednesday.
