The Dutch club stunned many by knocking out Madrid in the round of 16 after victory at the Santiago Bernabeu.
Following a 2-1 first-leg loss that saw Sergio Ramos intentionally take a yellow card to earn a suspension for the second leg, Ajax smashed Madrid in Spain, winning 4-1 to push their way into the quarter-finals.
Krol says that result was caused by Real Madrid's mentality as well as Ajax's talent, but the upcoming quarter-final battle with Juventus will be an entirely different situation.
"It will be more difficult against Juventus, that's for sure. Because in the round of 16, Real didn't approach this game with the right mentality," Krol told Goal.
"We have seen this with the yellow taken by Sergio Ramos. He thought the second leg would be easy. Moreover, at Madrid, Ajax had nothing to lose.
"Juventus is another team. And Ajax will no longer be able to count on the surprise effect.
"Anyway, if they want to beat Juventus, they will have to produce the same game as against Real. But everything will also depend on whether Ronaldo plays or not.
"He is a player from another dimension. He is a phenomenon in the box and, if he does not play, the task will be less easy for Juve. Because with him, even the other players take advantage of his presence and the fact that he attracts the attention of the opponents."
Krol went on to add that he is not surprised by Ajax's success this season.
As with years past, the Dutch team are built around young, up-and-coming talent with Frenkie de Jong and Matthijs de Ligt considered two of the most promising players in world football.
Add in star players like Dusan Tadic and Hakim Ziyech, and Ajax have a team capable of going toe-to-toe with even the Real Madrids and Juves of the world.
"Surprised? No. I saw the style of play that this team produces, and especially in the two games against Real, I must admit that it's good," Krol said.
"There are many young people surrounded by some players with more experience. They perform well and produce excellent football.
"Young people are not yet fully mature, but they are progressing together and are all very versatile."
Next season, the process will start over again for a club frequently rebuilding from within.
De Jong is bound for Barcelona while De Ligt is almost certain to leave for a massive transfer fee, but Krol says the club will rebuild as they always have.
"De Jong and De Ligt are going to leave, and maybe even two or three other players. It's inevitable at Ajax," he said.
"But the good thing is that they get a lot of money back. And it's important to be able to reinvest.
"They have already got their hands on a young Romanian [Razvan Marin] for next season, to replace De Jong. And there will also be a need to strengthen in defence, by recruiting someone or betting on a young player from the club."