Elanga scored with his first touch in the 80th minute after coming off the bench to earn United a 1-1 draw in the first leg of their Champions League round of 16 tie.
It was their first and only shot on target as Elanga became the club's youngest ever goalscorer in the knockout stages of the Champions League at 19 years and 302 days.
"I have dreamt of moments like this, scoring in the Champions League against top European teams like Atletico Madrid, [it is] a dream come true," Elanga told BT Sport.
"I think it was my first touch as well. He [Rangnick] said to me to make the defenders scared and run in behind.
"When I get the opportunity to take it. I wanted a good result for the fans because they came a long way.
"It is only the first half, we have to be ready for the second half at Old Trafford."
The Sweden Under-21 international has become a key part of the squad since Rangnick's arrival as interim boss in December.
His goal against Atletico, which cancelled out Joao Felix's seventh-minute header, was his second in successive games after again scoring as a substitute in the 4-2 win over Leeds United at Elland Road on Sunday.
"I told you how calm and cool I am and whenever I am given an opportunity I want to repay the manager and give 150% everytime I step onto the pitch," he said.
"I just do what I can do, I want to be the best player on the pitch and I appreciate the boss.
"You have got to stay in the game, anything can happen. We did not play the best in the first half, but improved after the substitutions in the second half."
United were fortunate to still be in the game when Elanga scored after a first-half performance Rangnick said he "couldn't believe."
Atletico twice hit the woodwork but United ended the game as the stronger of the two teams after Rangnick made a series of changes, including bringing on Elanga for Marcus Rashford.
"I don't know if I rescued it but after the performance in the first half, it could only get better," Rangnick said.
"What we played in the first half I still cannot believe. We played without conviction, without aggression and that is why we were struggling. We have to play better in the first half, I was very disappointed by that performance in the first half.
"He [Elanga] is playing as though it is a dream come true, it is a joy and fun to watch him play. I wish a few other players would take him as an example and as a role model."