Yes, that's correct. Assuming the speed of the cache doesn't change, a cache miss takes a fixed amount of time, and if the number of instructions per time unit increases, then more instructions get delayed because of the cache miss.
Modern processors try different methods to counteract this. Obviously you can use bigger caches which may lead to fewer cache misses. The disadvantage is that with the same technology, a bigger cache will run slower. Another method is organising the cache in such a way that "normal" code doesn't produce unneeded cache misses.
Another method is "streaming", where the cache figures out that you are reading from consecutive memory addresses, and uses this to start loading data before it is needed, reducing the average cost of a cache miss. That is often automatically. There may be instructions that load data from memory without caching it - if you process a gigabyte of data in consecutive memory, then caching any of it is pointless.
Then comes out-of-order execution: You may have one instruction waiting because of a cache miss, but other instructions not affected by this can go on executing. And with hyperthreading the processor executes two or more threads interleaving instructions; if thread A has to wait, then thread B continues at full speed.