I will try to answer this question from within Bible.
As I see it from Bible, some places it is not specifically mentioned that people who were healed had proclaimed their faith in Christ. This is at Mathew: 4:23, Mathew: 12:15, 14.14, Luke: 7:18.
Whereas some places even when there is no faith amongst the audience or the healed person, the healings have taken place. This is evident in the Verses Mathew12.9-13:
Mathew: 12:9 Then Jesus left that place and entered their synagogue. 12:10 A man was there who had a withered hand. And they asked Jesus, “Is it lawful to heal on the Sabbath?” so that they could accuse him. 12:11 He said to them, “Would not any one of you, if he had one sheep that fell into a pit on the Sabbath, take hold of it and lift it out? 12:12 How much more valuable is a person than a sheep! So it is lawful to do good on the Sabbath.” 12:13 Then he said to the man, “Stretch out your hand.” He stretched it out and it was restored, as healthy as the other.
Here in fact the audience certainly was without any faith in Him nor was the healed person expecting so. Similar instances are at Luke 14.1-6, Luke 16.19 etc,
Therefore, from this it can be averred that Jesus' power is not limited or relative to the belief of others. He can demonstrate His love to anyone He wishes to or anyone who wishes to draw close to Him. He was and is always full of power.
But then in verse 6.5, it is said that “Jesus was not able to do any miracles there except the healing of some sick people by laying his hands on them”.
Now as said in this verse He did perform healing of some sick people and those were also miracles. What the verse is saying is that He could not do many miracles except theses ones. He was not able to do any other miracles not because he was not having power to do so but because of their lack of faith and He exercised this option with His own authority not because he lacked power.
Also in the light of Mathew 12.9-13, this becomes clear in the following verse of Luke.
In Luke we see at verse 23:8
“When Herod saw Jesus, he was very glad, for he had long desired to see him, because he had heard about him and was hoping to see him perform some miraculous sign. 23:9 So Herod questioned him at considerable length; Jesus gave him no answer. 23:10 The chief priests and the experts in the law were there, vehemently accusing him. 23:11 Even Herod with his soldiers treated him with contempt and mocked him. Then, dressing him in elegant clothes, Herod sent him back to Pilate.
This gives inkling as to why in some instances, Jesus restricted by His own authority, the demonstration of his healing powers. Here Herod certainly was a man without faith and yet longing to see Jesus perform miracles. For him it was just some sort of public performance of Jesus’ powers. For some instead of filling with faith, they compare it to acts akin to some form of magic or to evil spirit. And we already have this in verse at: Mathew 12:22.
Mathew 12:22 Then they brought to him a demon-possessed man who was blind and mute. Jesus healed him so that he could speak and see. 12:23 All the crowds were amazed and said, “Could this one be the Son of David?” 12:24 But when the Pharisees heard this they said, “He does not cast out demons except by the power of Beelzebul, the ruler of demons!”