Gonzalo Higuain's equalised after the visitors had fallen behind but los Blancos could not build on the Argentine's strike and prolong the inevitability of losing their league crown to the Catalans.
"First of all, I want to congratulate Barcelona, their coaches, their players, their fans," the 50-year-old responded to reporters after the match.
"I think the logical thing to do is congratulate them. Last year we won and spoke of a great title achieved, and now I think it makes sense and is the least we can do to give due importance to their achievement.
A portion of the trainer's praise stemmed from efforts to deflect attention away from Pepe, who was dropped from the side after criticising his compatriot's treatment of captain Iker Casillas.
"You are always talking about a player and it does not seem relevant. The league has a new champion and you're talking about a player. I'm the coach. I don't need to justify anything," Mourinho responded.
"From the first to the last day I'll always decide who plays. I have the option of sometimes sharing the reasons for my decisions and other times, not."
The issue was made more pressing with the news that defender Raphael Varane looks likely to miss the Copa del Rey final against neighbours Atletico next Friday, although Mourinho did not appear concerned.
"On Friday, you'll see who plays and that will always be my decision and responsibility. Half my medical staff say Varane will not make the cup final.
"Obviously he cannot be in a game that everyone would want to play, but let's not dramatise because we have solutions. There are alternatives."
