Я должен был предвидеть, что …
…we're clearly talking about something that didn't happen in the past.
If you are absolutely sure (from a larger context) that you are talking about a counterfactual event, then your Russian phrase is wrong. What is your source? If not a good book, then it's probably a case of hypercorrection (similar to an English "he invited my husband and I to lunch"), because there is indeed a "low literacy" marker of people using more "бы" than the grammar calls for, here's a description of such overuse.
Have a read if that huge article anyway, maybe 4.1 is your case - it still does require the particle.
To summarise the article, though:
Сослагательное наклонение обозначает ситуации, не существующие в реальном мире.
Сослагательное наклонение выражается аналитически с помощью частицы бы (б).
If you assume that "Я должен был предвидеть, что…" by itself indicates a counterfactual aspect, then perhaps it's your view on life that needs adjustment. Or at least your Russian grammar! ;)
Counterfactuality here doesn't follow from "Я должен был". In Russian the phrase is simply a factual statement about the past - he had to have foreseen (he didn't foresee, but still had to)