It's not stressed enough these days, in Christian circles and otherwise, but the absolute purity and holiness of God is what sets the standard for those who enter heaven. And the only thing that can make us worthy of entering a place of such holiness is the shed blood of Jesus. Not our works. Even our best deeds, and best intentions, fall short.
That being said, one does not just waltz into heaven, on a free ride, so to speak, because of their belief in Jesus and His work on the cross, no matter how they lived their lives. This is a misconception, that too many Christians take advantage of, thinking it's ok to lead a sinful life, because they're already "saved." They are saved from hell, yes, if their faith is genuine, but they are not saved from judgement. We will all be judged according to our deeds.
I understand how it may seem unfair that a good, moral person may not be able to enter heaven. Sometimes I even question how God could not accept someone simply on the basis of being good. But our perspective is limited, and skewed. God is not some bully in the sky----He is a loving being who created us for a purpose. That purpose is to love Him in return, to have a relationship with Him. If He created us just to be "good", then He'd have no problem letting every single good person have eternal life with Him. But "heaven", as I understand it, is not full of "good" people, in some paradise, living their lives much the same as they lived them on earth. "Heaven" as I understand it, is about spending eternity knowing, enjoying, and worshiping God. So, if we choose not to know or love God now, in this life, what makes us think we'd enjoy heaven? I do not know whether hell is literally a place of fire----but I am sure it's a place of complete and total separation from God. For eternity. So God leaves the choice up to us. He doesn't want simply a bunch of "good" people to spend eternity with Him----He wants a bunch of people who are passionately in love with Him. He desires our hearts more than anything else. Not our impressive list of good deeds.