That was the feeling of Prophet Noah, peace be upon him, when his son refused to board the ship with other believers. He was sad to see his son drown as a disbeliever, but that was God's will, and he eventually got over it
I assume the same would happen in Heaven as God would heal the sadness of believers seeing those they love who did not accept faith not admitted into Heaven
In fact, this is the case of the uncle of Prophet Muhammad, peace be upon him. His name was Abu Talib, and he protected the prophet in the early years from his enemies in Makkah but refused to accept faith. The prophet was sad for him as God informed him that he would be in Hell. Being the uncle of the prophet does not mean he will be admitted to Paradise if he does not believe.
As for those who have even a small amount of faith in their hearts, there is a hadith which states that Prophet Muhammad, peace be upon him, will intercede for them on the Day of Judgment, and his intercession will be accepted. The Prophet will himself go from Heaven to take them out of Hell, and God will forgive them and admit them into Heaven.