Benni McCarthy's Cape Town City ensured a repeat of last year's final by beating Sundowns 4-2 on penalties at Lucas Moripe on Sunday after a 1-1 aggregate scoreline.
Cup holders SuperSport United edged Kaizer Chiefs 1-0 at FNB Stadium on Saturday to advance 3-2 on aggregate under the watch of Kaitano Tembo.
Mosimane says he would prefer to see Tembo win a trophy in what is his first season as a head coach, having recently been promoted from caretaker boss of Matsatsantsa.
"It's not about losing the match and having sour grapes," Mosimane said.
"As much as I wish him [McCarthy] the best and want him to win, I also want Kaitano, who has been with me for many years at SuperSport as my player, student - I also want him to win his first trophy.
"Because I want him to cement his position as SuperSport United head coach because the match is important to him.
"I can't win everything, other people have to win also. I will win next time, it's football."
It's been a tough spell for Downs, who also exited the CAF Champions League last week in the group stages.
Mosimane added: "It's not about winning and winning. You got to learn and let the team settle. I know supporters are little bit not happy but it's always good to wobble a little bit and come back.
"Two months ago you were raising a trophy then nothing, then the pressure mounts. They can only remember what happened two months back. You know the story, we spoilt them because we always want to lift trophies but we can't have them all."
The Brazilians next visit Golden Arrows in the league at Princess Magogo Stadium on September 19.