He had also been taken off in the early stages of the 1-1 draw with Barcelona the week before, with his fitness in serious doubt for the competition this summer.
"We would like it if, on the second [of June] everyone is ready to train," Del Bosque told ESPN.
"We cannot bring players who are lacking fitness.
"The World Cup begins on the first day and we want all the players to be in good condition, so that they can play the game against Holland on June 13."
Costa was born in Brazil, but pledged his allegiance to La Roja towards the end of 2013.
Spain face Bolivia in a friendly on Friday, but Costa will not be involved.