Ronaldo hurt by Madrid defeat
Jose Mourinho's side won their second leg 2-0 on Tuesday night but were still knocked out at the Bernabeu following a 4-3 aggregate loss.
Dortmund's Robert Lewandowski-inspired 4-1 first-leg win did the damage and Ronaldo acknowledged that fact.
But the Portuguese superstar still thinks he and his Real team-mates are the superior side, as he said: "The first leg was key but today we have demonstrated that we are a team that could be in the final.
"We missed chances. We scored too late. I want to congratulate the fans for their support.
"We have proven to be better than them but the score in the first leg was key. The fans have been awesome."
Late goals from Karim Benzema and Sergio Ramos gave Real hope in the second leg but Dortmund held on for their aggregate victory.
Jurgen Klopp's side will now meet either Barcelona or German rivals Bayern Munich at Wembley on 25th May.
Bayern hold a 4-0 lead over Barcelona after their first leg victory and will be confident of reaching the final ahead of Wednesday's second leg.