"As a result, the sequences [ti si di (d)zi] do not occur in native or Sino-Japanese vocabulary."[1] Unless I'm missing something, Japanese phonology doesn't include the sound english has as "si", only "shi"? I'm not a native speaker though, it's entirely possible that I am missing something.

[1] https://en.wikipedia.org/wiki/Japanese_phonology

Ah, you mean those sounds don't exist in (standard) Japanese? I got confused by you talking about "the English equivalent".