Silva said he was disappointed with his performance in last week's 1-1 first-leg draw in Madrid, so was thrilled to score the first two goals in the 4-0 win in Manchester that secured a 5-1 aggregate victory and a place in the Champions League final.
"It's a beautiful night for us. We knew it was going to be tough. But to beat this Madrid team 4-0 at home, it was wonderful," the Portuguese midfielder said pitch-side.
"A wonderful feeling to be in the final again, and hopefully this time we can try and win it," added Silva, whose team lost the Champions League final to Chelsea two years ago.
"My performance in the first game in Madrid wasn't the one I wanted, and I wanted to try and compensate for that because I didn't feel very good at all after the first game. And here today, I had to do better for my teammates and the fans.
"We were very resilient, we very passionate and organised at the same time. I'm so, so happy with that performance."
Silva effectively won the game for City with his first-half brace, one a shot, the other a header.
"I'm small, but I'm good with my head!" he laughed.
The English side will face Inter Milan in the final.
"They look very strong, very organised defensively and quick on the counter-attack," Silva said of the Italian side.
"It's going to be tough, but we're going to fight."
A SUPERIOR OPPONENT
Real Madrid defender Dani Carvajal was gracious in defeat.
"The opponents were better than us in the second leg, they have outplayed us by a large margin. They were a superior opponent," he told Spain's Movistar Plus TV.
"We lacked a little ... I wouldn't say attitude, but we closed back down too early. After the break, we had our best minutes. We'll come back stronger and we'll work next year to come back here.
"We knew that they are very strong at home, but after the sensations of the first leg, we all thought we could play a better game. We have very young players, with the desire to achieve a lot of success."
Manchester City's Jack Grealish, who tormented the Spaniards from the wing at the Etihad Stadium, said he had always dreamed of playing in the Champions League.
"It's unbelievable ... I don't think a lot of teams would do that to Real Madrid," he said.
"I don't know what it is, but it feels unstoppable."
Defender Kyle Walker, who matched Real's speedy forward Vinicius Jr for pace and kept him quiet all evening, said it had been a tough game.
"I thought the lads dug in well, they controlled the ball really well, especially in the first half ... We got over the line and that's the main thing," he said.
Matching Vinicius required immense self-belief.
"You've got to have a little bit of arrogance like the attackers do," Walker said. "I always say go toe-to-toe with them, I use my pace."
