They didn't. Solar powered calculators appeared in the late 1970s. Sony introduced the first transistor calculator in 1964, and 'pocket' calculators began to appear in the early 1970s.

EDIT: for example, here is a picture of a Bowmar 801b calculator, introduced in 1971. The off/on switch is the top right most switch (although only the "on" state is labeled.)

They could have had an off button but well... the calculators weren't backlit which means you couldn't use them with out a source of light.

Either the calculator had unlimited power (thus no need for a power button) or you were trying to use it in the dark and couldn't because of vision.

Calculators that ran on batteries had off buttons.

edit: thought this was ELI5