The Super Eagles' run was ended by France in their round of 16 clash.
Odemwingie said: "We go out in the second round but a lot of great teams were already at home watching the competition on TV.
"I think we can be proud of how we've done and for a long time we thought we could win.
"This is football, things can change quickly and at any moment. Unfortunately there was a little mistake when Vincent (Enyeama)... (pushed a cross to Pogba).
"But Vincent played a great game. But for him we might have been two or three down already. We knew he could save us and he did many times."
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