The Black Stars would have become the first African team to reach the semi-finals of a Fifa World Cup in the event of a win against the South Americans.
However, Dominic Adiyiah's goal-ward header was parried by Luis Suarez, who offensively used his hands, leading to a red card and a penalty for Ghana.
Gyan missed the spot kick as his team went on to lose the eventual penalty shootouts 4-2 following an overall stalemate.
"A lot of players miss penalties but sometimes people feel like that moment was crucial. The question I want to ask is that what about me being on the field, how would I feel after missing it? "Gyan said at the LEAD Series in Accra over the weekend.
"Sometimes things happen in the game and you face a lot of the ups and downs but it is something you cannot change. I am always trying to be a better man and sometimes when I'm alone in my room, I just think about all these things.
"I wish it could be rewound but it has happened. It's going to live with me for the rest of my life. Something can happen like it again and I can redeem myself or maybe my son or nephew is going to do it in the future and you might never know. But if it doesn't happen like that then I'm going to live with it for the rest of my life," he added.
Gyan is Ghana's all-time most capped player and topscorer with 51 goals in 105 appearances. He is also the African player with most goals, six, at the Fifa World Cup.