Prior to Friday's match, which marked the clubs' first encounter since La Celeste claimed a memorable World Cup quarterfinal victory in 2010, Asamoah Gyan had a chance to win a penalty when Luis Suarez was sent off for a goal-line handball.
Giorgian de Arrascaeta scored twice as Uruguay defeated Portugal 2-0. Paulo Bento's team secured second place in the group, though, thanks to South Korea's dramatic 2-1 victory over Portugal in the other game.
Daniel Amartey told reporters after the game that once South Korea won, Ghana was motivated to knock Uruguay out of the competition with them.
However, Addo emphasised that Ghana's strategy was unaffected by any hostility between the sides, saying: "I'm not sure who said it, but no one informed them about the [South Korea] score.
"I don't know how they would know. For us, it was about trying to score. As a coach for more than 12 years, I have had games where we led 3-0 and lost 4-3. Anything can happen.
"I don't think anyone was thinking about this, but I definitely wasn't. Everyone saw wild games with goals in the last minutes. We just wanted to equalise, which would have gotten us through."
Asked whether his players were motivated by a desire to avenge the 2010 defeat, Addo responded: "What hurts the most is that we're out.
"I know the public sought revenge but I don't think this way, and I told the players they should not as well.
"I am a strong believer that if you do not seek revenge, you will get more blessings. If it was not Uruguay, we would have tried against another team.
"It was not important. We were prepared, but today the luck was not on our side. We could have prevented both goals, this is where we have to learn.
"Sometimes you are so close to taking one step further, but then you concede and it gets into your mind. To come back out of this is very difficult.
"We did it against South Korea but today we couldn't do it, the second goal came way too early.
"We created a lot of chances, at the end we could have conceded a third goal. I believed until the end that we could score."
Uruguay failed to go past the group stage for the first time since 2002, while Ghana failed to do so at either of their last two World Cups (in 2014 and 2022).