The Chelsea midfielder claimed referee Mark Geiger saw Giroud strike him in a 29th-minute tangle but opted against showing the Arsenal man a card before France battled to a 2-0 win and a place in the quarter-finals.
Mikel told Mirror Sport: “Yes I got an elbow and the referee saw it and he only gave him a warning, not even a yellow card, nothing. 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.
"I don't think Giroud is a dirty player, I have played against him several times before and everyone wants to win for his country. He hasn't done those sort of things before so maybe it was just one of those things in the heat of the moment."
It was an even more painful match for Mikel's midfield colleague Ogenyi Onazi, who left on a stretcher during the second half following a challenge with Blaise Matuidi.
Mikel reported a suspected broken ankle for Onazi and, although he refused to criticise Matuidi, the 27-year-old did not pass up the opportunity to question Geiger once more.
"I thought the referee didn't help us at all. There were some heavy challenges and I think Ogenyi Onazi has broken his ankle. Challenges like this are bad but it was a 50-50, he just miscalculated," Mikel said.
France will play Germany in Rio on Friday thanks to Paul Pogba's 79th-minute header and a stoppage-time own goal from Joseph Yobo.
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