Going into the December break, Real Madrid trail Barcelona by four points in LaLiga standings having lost two and drawn three of their 18 league games so far this season.
Los Blancos are turning things around, though, and have won their last three matches in a row. However, despite their changing fortunes, there are still plenty of critics calling for Alonso to be sacked as head coach.
"The most difficult thing as a coach is to train in Madrid. It's a different pressure," Kroos said in an interview with Marca.
"Here you can win games and no one is happy. There are few clubs like that. In addition, if you draw or lose, which has happened lately, the reactions are different because the club is not used to this and the criticism increases.
"You always need results, but I'm convinced that Xabi is a very good coach and that he has the quality to train in Madrid, you have to give time. But we all know what Real Madrid means - Xabi more than most, and he knew before signing here what could happen."
Real Madrid return to LaLiga action with a home game against Real Betis and anything other than a comfortable win is sure to raise the pressure Alonso will be feeling.