The Argentine coach, who took over after the dismissal of Julen Lopetegui earlier the season, has suffered through four straight home defeats.
In the processes Madrid have lost all hopes at trophies for the season, having been knocked out of the Cope del Rey by Barcelona, fallen 12-points back of their eternal rivals in the Liga table and lost out at first knockout stage in the Champions League to Dutch side Ajax following a shocking 4-1 result at home in the second leg.
That is more than enough to see the pressure mount on any Madrid boss, but Solari says he has no plans to walk away despite all of the high hopes of the season being lost.
"I didn't come here to give up," he told a post-match press conference.
Defender Dani Carvajal had earlier claimed that the season was effectively over and that it had been a “sh*t” campaign for the club.
But Solari was not willing to chastise his full-back even as he tried to keep hope alive for a late push to chase down Barcelona in the league table.
"Carvajal has a lot of character, he was speaking in the heat of the moment on the side of the pitch,” he said of the comments.
“The season goes on, we've still got La Liga."
Solari also called for his side to “show bravery” as the club faces one of their most challenging times in recent memory.
"The season is difficult, but we are here to show our heart and character in difficult moments,” he said. “Easy moments are easy for everyone, you can climb up and surf them, but difficult moments you have to show bravery."
Before Tuesday, Madrid had only fallen to four straight home losses on two other occasions in the club’s history, and the loss to Ajax is the joint-heaviest the club has ever suffered at home in European competition.
If there is to be a turnaround of any sort it will need to come quickly, with trip to face Real Valladolid in the league slated for Sunday.