"To win a title is important for me," Koeman said. "Despite the changes at the club and the young players, at Barca you have to always fight for trophies.
"We have the first one and now we are going to fight to the last game in La Liga."
Saturday's victory was earned with four second-half goals, with Antoine Grizemann breaking the deadlock on the hour mark.
"A result like this is not normal, but we deserved the cup," Koeman said.
"It took us a bit to score, but we had chances. Our possession has been good and after 1-0 we have dominated the game with great football in every way."
The 58-year-old former Netherlands coach also heaped praise on De Jong and Messi for their leading role.
"De Jong and Messi are great players: Leo has been proving for so many years that he is the best in the world, he has returned to being effective, but we must also highlight Frenkie and the whole team," Koeman said.
"We have been at an extraordinary level. We deserve this cup."