Pressure is mounting in Benitez after the Selhurst Park defeat and while Aldridge believes the club will stand by him for now, he is not convinced the Spaniard who led Liverpool to Champions League glory 16 years ago can still succeed in the modern game.
"They have paid out a lot of money and a lot of it has gone down the drain," Aldridge told sundayworld.com.
"Benitez has got players there who have played under three or four different managers, but I think they have to stick with him. He's going to need money and they have got money. They need some positivity until the new stadium comes along.
"Over the years, Benitez has had a certain way of playing and it has aged, for me.
"You have got new managers like Jurgen Klopp, Pep (Guardiola) and (Thomas) Tuchel and then you look at Rafa and the way he plays is a little but dated, in my opinion.
"He is a good coach, but can he take Everton to the next level? I don't think he can."
Benitez was booed by the travelling Everton fans after he made the decision to bring off Richarlison in the 57th minute, but the Spaniard insisted afterwards it was due to the Brazilian having a slight calf injury.
“When you are disappointed because the team is not doing well, you can be emotional and react, but the reality is we made this substitution and we were right," he insisted. "Rondon came on, was holding the ball up and giving us something more.
"After he scored the goal but we try to do the best for the team every time. We make mistakes but we know the players, know how they are and try to make the right decisions.”
On the result which leaves Everton in 14th position, Benitez added: "When we were controlling, we make a mistake and concede the first goal.
"Second goal, another mistake. Third goal, another mistake. Good reaction with our goal, we have our chances and we didn’t take our chances."