Your enthusiasm and dedication are commendable, but you are misunderstanding the peer review process.
You are not a gatekeeper. You are a participant in a collaborative process to identify publishable papers and improve them. This process involves the authors, the peer reviewers (plural), and is mediated (if necessary) by the journal editor.
Let's talk only about papers which are accepted-with-revisions or minor-revise-and-resubmit. You and at least one other reviewer have made suggestions. The authors receive those and respond. When those suggestions are good ones, and they usually are, they address and/or incorporate them. In other cases, they respond, explaining why they didn't incorporate them, or why they addressed the underlying issue in a different way than a reviewer recommended. The rationale may be anything from the fact that the reviewer misunderstood (the response may then include clarifying some other language so others don't misunderstand), concern about scope creep or length, or just inconsistency between reviewer feedback.
For references in particular, there is a balance to be found from extensive and comprehensive literature review, through pointing to a set of representative articles anchoring the results in the broader field, to merely pointing to specific prior knowledge on whose shoulders the new results were developed. The authors may have just viewed it differently than you, or faced different feedback (e.g. even "this paper should cut down on the references, there are too many of them" from the 2nd reviewer).
If there is significant pushback from the authors, and/or disagreement between reviewers, the editor may send a revised version back to the reviewers. But that is up to them. It seems in this case they felt this was not necessary. Frankly, having briefly been an editor myself, if a reviewer made substantive suggestions, plus recommended a few additional references, and the author addressed the suggestions but pushed back with any reasonable explanation against the additional references, I would consider it a success and publish, as seems to have been the case.
What to do?
Regarding this paper, nothing. That ship has sailed. Unless omission of the papers creates a plagiarism situation, or truly egregiously omits the most important relevant reference in the field, no one is going to retract or print a correction about a potentially missing reference.
In the future, consider adding more explanation in your review why additions (whether literture or others) are important. This is for the benefit of both authors and editor. Shift from gatekeeper to persuader mindset. This might also affect your language more broadly. We don't know the context, of course, but personally I found your phrasing in the question, refering to "minor flaws" and "asked them to correct them" a bit concerning already. Perhaps it is appropriate, but as an erstwhile author, reviewer, and editor I would have preferred to see it positioned instead as "suggested improvements and recommendations", unless they are literally a gaping hole in the logic.
If you continue to find that certain journals and/or editors seem to pay insufficient attention to whether authors incorporate and/or address important reviewer feedback from you, refocus your time and energy on those who do.