The Argentine showed up more than an hour late for his news conference ahead of Sunday's La Liga game away to Real Valladolid, after a harrowing week for the team in which they were knocked out of the Champions League by Ajax Amsterdam.
Solari has lost his last three games in charge of Real, who are third in the league standings, 12 points behind leaders Barcelona and five back from second-placed Atletico Madrid, but practically assured of finishing in the top four.
"The majority have delivered as expected, some have not, and I have told them so personally," Solari told reporters on Saturday, after apologising for his late showing.
Solari took charge of Real on a temporary basis at the end of October when Julen Lopetegui was sacked and was then handed a contract until 2021.
According to reports in the Spanish media, he will be sacked next week. Solari would not comment on whether his job was in danger, but he made it clear that no coach can expect to stay at the 13-times European champions for long.
"I cannot reveal what has been said in private, but I will repeat what I said on my first day here, which is that everyone here is just passing through, and the only objective we work towards is the next game," he said.
"I'm always going to give the best of myself, as I have done since the first day I was here. It is an honour to coach Real Madrid."
Solari faces a selection crisis heading into the game against struggling Valladolid, above all in attack as forwards Lucas Vazquez, Vinicius Jr and Gareth Bale are all unavailable after sustaining injuries in Tuesday's 4-1 defeat by Ajax.
Defender Dani Carvajal is also injured as is midfielder Marcos Llorente, while captain Sergio Ramos is suspended.
(Reporting by Richard Martin; Editing by Christian Radnedge)
