Mourinho also took the opportunity to answer his critics after the 1-0 triumph while defender Sergio Ramos said the Madrid players were ready to follow their coach "to the death" such has been his impact at the club.
Barcelona great Johann Cruyff led recent criticism of Mourinho by claiming he only existed to pursue trophies and was not a "football coach".
Speaking after this triumph, Mourinho said he would take such words as a compliment. He said: "Winning titles is wining titles, it's always good. Only a few days ago someone called me a coach who wins titles and not football. Thank you. I like being a coach who wins titles."
Having lost his first Clasico 5-0 at the Nou Camp last year, Mourinho's men earned a draw in their return league clash at the weekend before this breakthrough victory. That is a trend in Real's favour that Mourinho believes stands them in good stead for their upcoming Champions League semi-final tie over two legs.
"I am thrilled to win the Copa del Rey - it is something special. It's a fantastic triumph against a great team like Barcelona - and we deserved it. We can take them on over two games; we have just done that. There is no reason we can't beat them in the Champions League because we have just drawn once against them and then beaten them. I came here to do a job and change the mentality of the club. We have started to do that and it's satisfying - but it's just the start.''
Right-back Ramos said of his coach: "Mourinho is the captain of our ship and we are with him to the death. What he is trying to instill in us is working wonderfully."
Meanwhile, Zinedine Zidane, the last man to score a winning goal for Madrid in a cup final - during the 2002 Champions League final - echoed those sentiments.
"This is an important trophy because it's the first trophy in a long time and the club needed it,'' Zidane, now a special advisor at Madrid, told reporters after the game. "Now it will give us confidence for the games against Barcelona.''
Ronaldo, the matchwinner, said he knew the first goal would prove crucial.
"We knew that whoever scored first would win it - and so it proved,'' he said. "Mourinho has given us a winning spirit and this is a really important trophy for us - it was an objective we had for this season and we have achieved it.''
Barcelona coach Pep Guardiola was philosophical in defeat after losing his first final as coach of the Catalan club.
"It's always better to win than to lose,'' Guardiola said after the game. "But life is like that - you can't always win.''
Despite failing to beat Madrid in their two meetings in the last few days Guardiola is adamant his side can bounce back.
"We will pick ourselves up - of course we will,'' he said. "We are more sad than if we had won, but that's part of the game. These players have been playing together for a long time and we'll bounce back.''
Midfielder Xavi added: "We still have the best two titles to play for.''