Mourinho’s side sealed their 32nd league crown thanks to goals from from Gonzalo Higuain, Mesut Ozil and Cristiano Ronaldo at the San Mames on Wednesday.
Madrid hold a seven-point lead over Barcelona, who won 4-1 against Malaga earlier in the day, with two games left to play.
Mourinho has now won league titles in four countries, after enjoying success with Porto, Chelsea and Internazionale before taking over at the Bernabéu.
“I won the league title in Portugal, Italy and England, but this one has been the toughest,” he told Real Madrid’s website.
“I’ve won seven league titles overall and I know what it feels like. Barcelona won all their games, as befits the great team that they are. They’ve been winning to the very last day.”
He added: “They are a club with great tradition that knows we deserved to win this title.”
Meanwhile, Ronaldo, who trails Lionel Messi in the La Liga goalscoring charts by two strikes on 44, could not hide his delight at Wednesday’s triumph.
“I am incredibly happy,” said Ronaldo. “This is my first league title in Spain and I am delighted.
“The league is even harder with a team like Barcelona, but we were better than them. We’ve achieved our objective and we’re all excited about winning La Liga.
“I have two Golden Boot awards at home. It would be nice to win another, but I wouldn’t mind it if I didn’t.”
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