The full-back produced an eye-catching display in the first leg of the last-16 tie at the Santiago Bernabeu.
Despite a nervy opening 45 minutes when he was asked questions by Cristiano Ronaldo, the 22 year-old improved after the break.
He thinks the Red Devils can now finish the job at Old Trafford to knock out Real, while he is hoping to get a recall to the national team after last appearing for A Selecao in their Olympic final defeat to Mexico.
"(Sir Alex) Ferguson talked to me at half-time because I was leaving some space behind me," Rafael told Globo Esporte. "I was a little anxious because I didn't feel that I was playing well, but I did improve a lot after the break.
"We now have the advantage. It's like it is still goalless and we have the home leg to come, but I still think we could have won the game. We now have a great chance of advancing to the next round.
"Of course my goal is to play for the national team again, especially because I am a starter for Manchester United. I wasn't called up for the last international (against England) but if I keep playing well, my time will come."