The Super Eagles had worked themselves back into a position to make the last 16 of World Cup 2018 after responding positively to an early opener from Lionel Messi.
Victor Moses had restored parity after calmly slotting home from the spot, but could have been given the chance to double his tally from 12 yards had the match officials not waved away handball protests.
Late on, Rojo rose inside his own box and headed the ball against his own arm, leading to vociferous protests from Nigeria and consultation with VAR.
Play was eventually allowed to continue, with Argentina’s Manchester United defender going on to snatch an 86th-minute winner, but Mikel was refusing to let the issue lie at the final whistle.
He told reporters: "It was a clear penalty for me.
“If you look at the Portugal game yesterday, this wasn't close to that. This was worse. We have seen it again in the dressing room. It was a clear handball.”
Iran were awarded a penalty during a meeting with Portugal on Monday after Sardar Azmoun nodded the ball onto the arm of Cedric.
Technology was also used in that incident, but Nigeria missed out on getting a favourable call 24 hours later.
Mikel, as captain of his country, led the discussion with referee Cuneyt Cakir and, despite appearing to have been informed that the ball had struck Rojo’s head first, the former Chelsea midfielder claims to have received no suitable explanation as to why a spot kick was not given.
He added: “The referee looked at the VAR. He said it hit the hand. I asked why he didn't give the penalty, but he said he didn't know.”
Argentina, meanwhile, have recovered from a slow start to their campaign to book a last-16 clash with France.