Kroos enjoyed a strong game for Madrid as he started alongside the Spain veteran in the 1-1 Supercopa de Espana first-leg draw against Atletico Madrid.
Kroos almost scored in the second half, volleying over the bar, before playing a part in James Rodriguez's scrappy goal, and Alonso stated after the match that the Germany international will prove a valuable acquisition for the club.
"It's easy to play with big players like him," Alonso was quoted as saying by AS.
"Despite his youth he has experience at the highest level and is a great signing for the club."
James's 81st-minute opener was cancelled out by Raul Garcia's goal as Atletico took the upper hand heading into Friday's Supercopa second leg but Alonso maintains the tie is still wide open.
"They [Atletico] demanded a lot of us and are very compact. It's a strategy they're good at," he added.
"They drew level and it could have been a better result for us but it's still open for the return."