Robert Lewandowski fired four goals as Dortmund emulated fellow Germans Bayern Munich's Champions League semi-final domination of Spanish opposition.
Asked if a place in the final was still a realistic possibility, Mourinho told Sky Sports 1: "It is of course very difficult but in football it can happen. Of course we can, on a crazy night, where everyone performs at a high level and every chance you have and every goal you score is with a high level of efficiency. Of course you can."
He added: "I think they were the best team by far and won every individual battle on the pitch and were stronger than us, more aggressive physically and tougher mentally so they deserved it.
"How it went from 1-1 to 4-1, I really don't know because everything happened in a very short space of time in the far goal from the position where I was. But we lost easy possession and we couldn't cope with their counter-attacking and their transition.
"We prepared for the game so well, in every detail, as we always do, especially in a semi-final. We prepared for everything, we were ready for everything.
"We are very confident about the work we did. I think many of the boys didn't perform and many of the boys didn't have a good night and this is exactly when you cannot make mistakes because at club level this is the second most important match in the world of football.
"The first one is the Champions league final, the second one is the Champions League semi-final so when you don't perform on a very special day it is very disappointing."
Dortmund manager Jurgen Klopp hailed his side's performance against the visiting Spanish giants.
He said: "It was an unbelievable, great game of my team. It was so difficult today because they are so strong and fast and they are so brilliant on the counter-attack."
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