That victory meant the champions broke a league record by reaching 100 points for the season, but Mourinho insists the demands of managing such a big club means there is no time to rest on your laurels.
He told Real Madrid TV: "In this moment I am already thinking about the future, this is the time to finish the celebrations.
"They will end today [Sunday], the players will think about the Euros, and I will go to work and think about next season because at Real Madrid you can't sleep on what you have achieved. You have to think about the future."
Mourinho was joined by his players and staff as they paraded the trophy at the Madrid Town Hall today [Monday], and club president Florentino Perez also promised to deliver more trophies in the coming years.
He told Marca: "This team has achieved a collective feat that will remain in the memory of all Madrid fans.
"The merit goes to a formidable squad and a great coach who already form part of the history of this club with numbers that will be difficult to forget.
"It is an honour to return here with the work completed. A year ago (after winning the Copa del Rey) we said we would return and here we are. We say the same for next year.
"This club was born to win, we never tire of doing so. We are going to work with tenacity to continue growing the legend of Real Madrid. This is our challenge."