The former Real Madrid player and director of football was speaking to Cadena SER's El Larguero after the club's 3-2 Champions League victory over AEK Athens, a result that maintained their 100 per cent record in the competition with 12 points from four matches.
Mijatović enjoyed the latest comeback but admitted he would prefer to see Madrid control matches rather than repeatedly having to rescue them.
"Another comeback. For the fans, these epic comebacks are very beautiful. But I would prefer to experience a calm match in which Real Madrid dominate from the first minute to the 90th and we don't have so much stress. Today, for example, we started very badly. Let's live a little more calmly, please, and enjoy the football. Fewer comebacks and more tranquillity," he said.
Mijatović believes Mourinho's strong position at the club has been important in restoring Valverde's confidence and performances. He argued that players are more willing to accept difficult decisions when they know the manager has the full backing of the board.
"When a player at a big club knows that he has a manager in front of him who has achieved everything and has a great personality, but also has the total backing of the club, the player will accept absolutely everything. Everything," he explained.
"If the players have doubts about whether the manager has the club's backing, those statements start: 'I can play here, but I wasn't born for this...' When they know the club supports the manager, they accept everything and want to play. They are reborn, so to speak. I experienced that as a footballer, and that's why I'm telling you."
He also praised Mourinho's management of a large squad, particularly the way he has kept fringe players motivated.
"Mourinho is achieving something very important: players who don't play much come onto the pitch happy, eager and wanting to show their best version. And that's key because the squad is large and, over the course of the season, you're going to need everyone."
Mijatović was less convinced by Vinícius' current form, suggesting the Brazilian is feeling the pressure now that he faces greater competition for his place.
"Watching the matches he has played so far, I see him suffering. Until now he didn't have competition and now he does, and you can see that. He's playing with a lot of pressure, he wants to be decisive in every moment and he's a long way from his best version. I think he needs to relax."
The former Madrid striker believes the forward can still become a decisive figure as the campaign progresses, but says he must put the summer's uncertainty behind him after committing his future to the club.
"Once you've made the decision to stay, you have to forget everything that has happened and concentrate on your best version. But I still believe he can give us a lot of joy."
Mijatović also singled out Jude Bellingham for praise, describing the midfielder as Madrid's best player against AEK. He said supporters should not judge Bellingham solely by the goalscoring numbers he produced when he first arrived.
"Fantastic. For me, Bellingham was the best on the pitch today. And not just today, I've been seeing him play very well in many matches. People miss those numbers because he scored so many goals when he arrived, but he has never been a goalscorer. What he's doing in these matches is what we need from him. And if he also scores, as he did today, then even better."