Jesus was aquainted with loneliness of a sort:
Luke 9:57 As they were walking along the road, someone said to him, “I will follow you wherever you go.” 9:58 Jesus said to him, “Foxes have dens and the birds in the sky have nests, but the Son of Man has no place to lay his head.”
The NET translation notes add: Jesus’ reply is simply this: Does the man understand the rejection he will be facing? Jesus has no home in the world (the Son of Man has no place to lay his head).
Many times Jesus would try and explain something to the disciples and they couldn't understand. And during the crucifixion his friends didn't stay awake with Him in Gethsemane and most left him at the cross.
So, I think in following Christ we can expect to be alone in different ways, as others don't understand what God has called us to do or what we go through is too hard for them to cope with.
If you've ever been left alone whilst going through something because the people around you couldn't handle it, then Christ knows what that is like and went through the same. We don't have to deny or hide such loneliness, we can allow ourselves to connect with Christ and allow His presence with us in our pain. (Which doesn't necessarily take the pain away, but it does mean we don't have to be alone with it.)
Is 53:3 "He was despised and rejected by men, a man of sorrows, and familiar with suffering. Like one from whom men hide their faces he was despised, and we esteemed him not."
