Cache Miss and Processor Speed

today in my class my professor mentioned that

Cache misses becomes more expensive as the speed of the processor increases 

But he didn’t explain the reason. I searched this statement over the internet and found no answer whatsoever.

According to me, this statement is true because, when the speed of the processor increases it can execute more instructions at a given clock cycle, thus a miss leads to a stoppage of more instructions from executing. So cache misses becomes expensive as processor speed increases. Is my thinking correct or am I doing it all wrong?