The verse in question does not highlight the transition from the Law and the Old Covenant to the fulfillment of redemption in the Messianic era. It states that to be a fact.
The verse in question does not illustrate the continuity and discontinuity between the two covenants within God's overarching plan for salvation. It states that to be a fact.
The question is asking about the doctrine of salvation (soteriology) but the verse in question cannot, in and of itself, express the reasons for the Law being but a shadow of the good things that came through Jesus Christ, and nor does it; it cannot express the reasons for the sacrifices demanded in the Law never making those submitting to that Law "perfect", and nor does it.
For those reasons, all of chapters 4, through to the end of 10 in Hebrews would need to be scrutinized, as well as a raft of other Bible texts that also explain how the Law (all of it, not 'just' the sacrificial system) was a pointer to Christ, a 'tutor' designed to lead people to faith in Christ, wherein only can 'perfection' be found.
This answer would stress that nobody here (so far, including myself) is claiming, or even suggesting, that the Law of the old covenant was useless. It was fulfilled, in Christ. It served its purpose, so that a new way was opened up to those desiring to be acceptable to God. No longer would annual sacrifices of animals be needed, for the one perfect sacrifice had been made, in Christ. That is what the verse following the verse in question explains, so that a hermeneutic answer needs to start with verse 2. It begins with "For" showing its continuity with verse 1, which also starts with 'For' showing it continues from the previous chapter:
"For the law having a shadow of good things to come and not the very
image of the things, can never with those sacrifices which they
offered year by year continually make the comers thereunto perfect,
(2) for then would they not have ceased to be offered? because that
the worshippers once purged should have had no more conscience of
sins." Hebrews 10:1-2 A.V.
The verse in question can only be a spring-board into the massive depths of the soteriological significance of how the old covenant Law led into the new covenant law of the Spirit of life in Christ Jesus - Romans 8:2 & 10:4. The Law itself showed the futility of seeking salvation by works, so that when the New Covenant in Christ came, it set forth another way of salvation altogether, that of faith in Christ, and believers in him would discover release from legalistic works. I have in my notepad a list of 50 texts that delve into that aspect of soteriology - the Law now being superseded by Christ fulfilling it. Of course, that is a topic, and not for the Hermeneutices site. I must stick to the verse in question, and trust this answer will suffice.