Two late goals allowed France to book their spot in the quarter-finals, but Mikel was left frustrated after the game due to Mark Geiger's failure to address the clash with Giroud.
"Yes I got an elbow and the referee saw it and he only gave him a warning, not even a yellow card, nothing," the Chelsea midfielder told The Mirror. "It was bad.
"We know the game - if you see it, act on it. The ref saw it. He did catch me, I don't know if it was too hard but the intention was definitely there."
Nigeria head coach Stephen Keshi was also critical of Geiger's display in Brasilia.