The 20-year-old was told to stay on the pitch and win the game after his first half penalty miss, which left him close to tears.
Paraguay came back, however, and beat Venezuela 2-1 to remain in contention for the World Cup in 2026 which manager Gustavo Alfaro says is due to squad mentality and a hunger to fight back even in the darkest moments.
“This was a match for men. I saw Messi, Maradona, Platini, great players miss penalties," said Alfaro.
“I saw none of those great players surrender. On the contrary, I saw them defy the adversity of fate.
“You want me to take you out or you want to come in the second half to work for the team?
“These are the battles that make you men, it has nothing to do with age, but with the spirit you have.
“The only thing I asked him is to believe, to keep insisting and to move forward."
Enciso revealed why he asked to be taken off after the game in an emotional interview afterwards.
"The coach supported me from the first day, he told me that I was one of the players that he really likes and that motivated me to be able to come in. I told him to take me off, because I lost focus completely.
“When I didn't score the goal, I fell apart. Luckily, we were able to turn things around and give the country some joy. ”I appreciate the support I have from my team-mates. The group we have is incredible.
“The truth is that everyone supported me and thank God I was able to enter the second half differently.
“Missing a penalty is very difficult for a player, even more so with my national team, the country that I love so much. The truth is that it was very bad.”
Paraguay now sit sixth in the World Cup qualification group and have lost just once in 5 games as they make their way up the table towards a place in the biggest tournament in football.