The Super Eagles were minutes away from securing a point against the Albiceleste which would have seen them take second place in Group D.
The result means that Nigeria finish third in Group D and will play no further part in the competition, but despite the heartbreak, Mikel is proud of how his team has performed in Russia.
"It is what it is," the Tianjin TEDA midfielder told reporters at full time. "We did everything we could.
"In the second half we pushed and pushed. It just wasn't to be. It's a young team and in four years most of them will be ready for this tournament.
"I'm very proud of the boys and what we have achieved. I think we have done really well. We have to keep going. Thanks to all the Nigerians who have supported us."
Nigeria return to action in September with an Africa Cup of Nations qualifier against Seychelles.