What Jesus said was that he came not to abolish the old laws but to
fulfill them.
Another thing Jesus said about the Old Testament law was that it was a lowered standard. "You have heard it said" not to murder, but Jesus said being angry (unjustly) is committing murder in your heart. In the same way, lust is like adultery.
And again, in conversation about divorce, the religious leaders of his day told Jesus that Moses allowed them to divorce, but Jesus said "Moses gave you this law because your hearts were hard".
So it's clear that in Jesus' eyes, the OT law was not the ultimate moral standard, which he said was summarized in "love the Lord your God with all your heart, soul, mind and strength" and "love your neighbor as yourself". If we truly did those things, of course we'd not murder, etc.
It's a bit like rules for children. I tell my toddler not to pull his sister's leg, but I want him to someday mature to the point where he doesn't need that rule, because he loves her and wants what's best for her.
The OT law, with its low standards, was still too hard for humans to keep, pointing to the need for Jesus to fulfill it for us - and He fulfilled not just the low-standard law, but the true one.