Where would space exploration be without the invention of the transistor?

NASA's space exploration technology seems to do astounding new things each year, as we were reminded by the IEEE Spectrum article  NASA’s DART Mission Aims to Save the World. 

Surely, NASA's people deserve great credit for those developments. However, a colleague recently told me he thought the development of space technology would have stalled decades ago if it had not been for the invention of the transistor.

Does the transistor deserve much more credit for the development of space technology? What is your opinion?