Curci believes Karius was favoured by Mainz management when the pair were together in Germany.
Now playing in Sweden for AFC Eskilstuna, the Italian goalkeeper told TMW: "I was back-up at Mainz.
"It was mainly the choice of the club, because they wanted to increase the value of the player. He could make a lot of money for the club at the time. That's how it went. Karius has been very lucky, but happiness is not always on your side.
"And as far as the final of the Champions League is concerned, he has proved that he is not ready for that level. The error for the third hit (by Gareth Bale) can still happen. He has misjudged the ball, a mistake that every goalkeeper can make.
"But the first? No definitely not. Even my nine-year-old son cannot afford that mistake."