The Spanish forward was on target for the Old Lady, yet his equaliser was not enough as Barca ended as 3-1 winners to record their fifth Champions League victory, and their fourth in the last nine years.
The 22-year-old said he is still struggling to come to terms with the defeat, wishing to forget all memories and recollections of Saturday night’s match.
“These have been difficult days,” Morata told Cadena Ser.
“Losing a Champions League final is a big deal. Before the final, I got up in the night a few times thinking I’d already played the final, it was a dream for me, I couldn’t wait.
“At the end, I didn’t swap shirts with anyone. I don’t want any memory of that day. I didn’t even take the medal, I don’t have silver medals at home.
“Credit to Barcelona though, and their coach, we have to know how to lose too.”
The former Real Madrid frontman has denied speculation that he will be returning to Los Blancos next season, insisting he is happy in Turin where he has steadily improved his game.
“Nobody has told me anything in Madrid, the only one who talks of my return is my grandmother,” he said.
“It’s been a very good year for me in Italy, and need to give even more to Juve. I’m happy at Juventus.
“I’ve improved a lot physically in Italy, we work very hard on that side of the game. I get to the training ground at 9.30, and I leave at 15.30.”
Morata has been included in the Spanish squad that is currently preparing for their Euro 2016 qualifier against Belarus on Sunday.