His responses are important for us because the same thing happens today. Jesus stayed focused on the will of the Father: bringing hope to a sin-soaked world. He said it is the Father's testimony and the testimony of the (completed) work the Father assigns that matters.
What Jesus did not do is important to see as well. He said that He does not accuse folks to the Father--that the things that folks trust in other than Him will do their own work. He did not stress over what others thought and said. Jesus simply pressed on and taught through the difficulties.
However, the scriptures say He actually looked in anger at one point, though, so we must take notice of that. Hard-hearts made Jesus angry. Hard hearts also preceded madness. There is great danger when our hearts are hard. I believe abrasions and wounds have a glorious purpose: to keep us from pridefully assuming we know it all. That we do not all agree is wonderful! But we must also remember another admonition of Jesus as He faced opposition: "I desire mercy and not sacrifice." He wants us to be the same. Mercy, not giving to others what they 'deserve,' is more important than the things we choose to sacrifice. When we face accusations and criticisms, we have a beautiful opportunity to let the abrasion keep us from being hard-hearted!
We, as Christians, only see in part. We glimpse Jesus from our own view. So what we do is stay focused on the will of the Father. What we do is extend mercy to those who hurt us. What we do is trust in the testimony of the Spirit in our heart and in the work God gives us to do. We won't always please people. We won't always be honored or feel special. Lord willing, we won't develop hard hearts either! To God be the glory in all our lives.