‘And he did not perform many mighty works there because of their unbelief.'
Jesus was able to accomplish very little in His own home area, simply because, in their unbelief, they did not come to Him or seek His help, apart that is from a few. (Mark states it slightly differently but says the same thing - Mark 6:5-6). Had He performed some unusual feat appropriate to an artisan they would have willingly shared with Him in His honour, but as far as they were concerned for Him as a carpenter to claim special inspiration from God was seen as disreputable and unacceptable, and they were therefore quite confident that all this talk about healings was a hoax. In view of that they did not bring their sick for healing, although the few who did were satisfied.
Note that Jesus will not perform wonders in order to gain attention. In the main His ‘mighty works' are a compassionate response to the needs of the people, not an attempt to win people. That is why they are Messianic signs. They reveal the compassion of the Messiah, not a desire to win people by signs. He is quite willing to concentrate on the preaching. he does not want men to follow Him just in order to see wonders (John 2:23-25).