Sections of the Santiago Bernabéu crowd whistled some Real Madrid players during the 2-1 Champions League win over Inter Milan, despite the team leading for most of the match.
Mijatović, speaking on Cadena SER's 'El Larguero', linked the reaction to years of pent-up frustration rather than anything specific to Tuesday's performance.
"It surprised me because we were winning, but it comes from two years back. People are already angry about not winning trophies in recent years, and it takes very little for them to whistle. They're not very happy," he said.
The former striker and sporting director argued the current squad has not yet convinced supporters it can challenge for the league title, pointing to the conduct of certain players as part of the problem.
"Madrid doesn't give guarantees that it has the team to win the league," he said, adding that fans' frustration was sometimes aimed at "the behaviour of certain players that at a given moment angers the crowd." He was nonetheless sympathetic to the players' position. "It's a lack of football, but the players have to keep doing their job despite having the crowd against them, and Mourinho has that quite clear," he said.
On the mark Mourinho is beginning to leave on this Real Madrid side, Mijatović urged patience.
"It's early, but you can sense a certain seriousness... Little by little Mou will achieve what he wants: a solid team, well organised, that's lethal on the counter-attack," he said. "Little by little. You have to be patient. You shouldn't judge them now after five matches played."
Asked about the club's ongoing search for creativity in midfield, and whether Bernardo Silva might be the solution, Mijatović pointed instead to a player Real Madrid narrowly missed out on.
"I still feel Real Madrid is missing a conductor... which could have been Rodri without any problem, but it wasn't to be, and they have to look for one within the squad," he said, referring to Barcelona's marquee summer signing. He also cautioned against comparing the current group to two Madrid legends.
"You shouldn't cry over players who are no longer here and who made history, like Luka Modrić and Toni Kroos. We miss them... but where do we find players like those two? You have to trust the ones who are already here and never compare them to Modrić and Kroos," he said.
"Madrid can improve, but people are agitated and protesting, and that will continue until the team shows something different."