So we’ve got the basics down. We all carry mutations in genes that are harmless by themselves, but if you get two broken copies of the same gene bad things happen. The answer to your question has to do with probabilities.
Let’s say you have two populations. In the first there are 100 genes with recessive lethal mutations, each at 1% frequency in the gene pool. This means that on average there is 1 recessive mutation per individual. The probability of an individual receiving 2 copies of a single recessive mutation assuming completely random shuffling is 100 * 0.01^2 (one hundred chances of getting two copies), or 1%.
Now let’s look at a population with only 10 recessive lethal mutations, but that are now at a frequency of 10% in the population. On average there is still only 1 recessive mutation per individual, but now if we calculate the chances of a person being born with two of the same mutation we get 10 * 0.1^2 which is 10%.
The two populations have the same total number of recessive lethal mutations, but problems arise more frequently in the second population. So while a populations bottleneck will remove the vast majority of genetic issues, the ones that remain will run rampant in the remaining population.