I am more inclined to translate the verse as: "Do not think I came to destroy the law or the Prophets but to complete (pléroó) them". In other words, the moral Law of the Prophets was a foundation but not yet the entire or complete way to salvation (because the moral law alone can result in spiritual 'death', such as burning in 'hell' if you get angry at a sinner or at your brother who sins).
As for those parts of Law Jesus said he would not abolish, this is explained in Matthew 19:16-22:
And behold, one came to Him and said, “Teacher, what good thing shall
I do that I may obtain eternal life?” 17 And He said to him, “Why are
you asking Me about what is good? There is only One who is good; but
if you wish to enter into life, keep the commandments.” 18 He said to
Him, “Which ones?” And Jesus said, “You shall not commit murder;
You shall not commit adultery; You shall not steal; You shall not bear
false witness; 19 Honor your father and mother, and You shall love
your neighbor as yourself.” 20 The young man said to Him, “All these
things I have kept; what am I still lacking?” 21 Jesus said to him,
“If you wish to be complete, go and sell your possessions and give to
the poor, and you shall have treasure in heaven; and come, follow Me.”
22 But when the young man heard this statement, he went away grieved;
for he was one who owned much property.” (The parallel passage is
found in Mark 10:17-22 and Luke 18:18-23, listed at end of the
Therefore, it appears Jesus was referring to the core fundamentals of the Law rather than the more superficial and dispensable tenants of what is now called Judaic or Talmudic Law.
Since Jesus said: "a time is coming when you will worship the Father neither on this mountain nor in Jerusalem... God is spirit and his worshipers must worship in the Spirit and in truth." (John 4.21), whether you worship on Saturday, Sunday, Easter or Passover is irrelevant to his Way.