"Unbelieving" can also mean doubtful.
Yet consider also what Jesus did for Thomas, who had refused to believe:
"Then saith he to Thomas, Reach hither thy finger, and behold my hands; and reach hither thy hand, and thrust it into my side: and be not faithless, but believing." (John 20: 27)
Jesus ministers to us, even when we are doubting. Faith is not something which we conjure up through our efforts, but rather something that we receive as we see Jesus.
Consider also the example of John the Baptist, who had witnessed Jesus baptized with the Holy Spirit:
"2Now when John had heard in the prison the works of Christ, he sent two of his disciples, 3And said unto him, Art thou he that should come, or do we look for another? 4Jesus answered and said unto them, Go and shew John again those things which ye do hear and see: 5The blind receive their sight, and the lame walk, the lepers are cleansed, and the deaf hear, the dead are raised up, and the poor have the gospel preached to them. 6And blessed is he, whosoever shall not be offended in me." (Matthew 11: 2-6)
Jesus offered John the Baptist verses of Scripture (specifically, Isaiah 35: 5-6). In Luke's Gospel, not only doe Jesus reference Scripture speaking of Himself, but He performs miracles in the same hour following the inquiry from John the Baptist's disciples:
"When the men were come unto him, they said, John Baptist hath sent us unto thee, saying, Art thou he that should come? or look we for another? 21And in that same hour he cured many of their infirmities and plagues, and of evil spirits; and unto many that were blind he gave sight. 22Then Jesus answering said unto them, Go your way, and tell John what things ye have seen and heard; how that the blind see, the lame walk, the lepers are cleansed, the deaf hear, the dead are raised, to the poor the gospel is preached. 23And blessed is he, whosoever shall not be offended in me." (Luke 7: 20-23)
When we doubt, we should never worry, nor should we feel ashamed, but instead we can rest in the sure testimony of God's Word, all of which testifies of Christ and Him Crucified:
"44And he said unto them, These are the words which I spake unto you, while I was yet with you, that all things must be fulfilled, which were written in the law of Moses, and in the prophets, and in the psalms, concerning me. 45Then opened he their understanding, that they might understand the scriptures, 46And said unto them, Thus it is written, and thus it behoved Christ to suffer, and to rise from the dead the third day: " (Luke 24: 44-46)
Don't Worry about Doubt, because you are not saved because of your works, but by Christ's death at the Cross. Even if you do doubt, the answer is found in receiving a greater revelation of Christ Jesus and Him Crucified, and so you can rest assured that even your doubts do not push God away, but rather invite Jesus to reveal Himself to you in a greater way!