The Brazilian, who spent eight years with the Red Devils before leaving in 2015, netted the penultimate penalty in United's famous victory in Moscow.
United went 5-4 ahead after Anderson, who came on as a substitute in extra time, beat Petr Cech before Salomon Kalou replied for Chelsea.
But United's victory was soon wrapped up after Edwin van der Sar denied Nicolas Anelka on the back of Ryan Giggs successfully converting for Sir Alex Ferguson's men.
And Anderson has since revealed that he was petrified ahead of his spot kick, telling Radio Grenal: “I came on to take the penalty. I hadn't touched the ball.
“I was sitting on the bench, Giggs looked and said: "Get Anderson to take one". I said "Oh my". I took the ball, it was the longest walk of my life.
“I came with the ball, there is no way I wouldn't be shaking. I was already shaking. I was terrified. The story of a club and our fans were on that side.
“I went to the ball, I got the ball, I looked at that goalkeeper, who is a giant. Cech opened his arms, I said "oh, I'm f*****", I'll kick it hard, close my eyes and pray for the ball to go in".
“Then I took three, four steps, I closed my eyes and the ball passed just by his hand.”
United's Champions League victory at the Luzhniki Stadium was just one of several honours lifted by Anderson during his trophy-laden spell at the club.
He also won four Premier League titles, two League Cups and also the FIFA Club World Cup before joining Brazilian side Internacional in 2015.