The Alter Rebbe was not ignoring the reality of pain. He was validating it. He calls the sadness a "great battle" ( Milchamah Gedolah ). He acknowledges that for the sufferer, this battle is harder than fasting or self-mortification.
For further study, explore the daily Tanya study cycle (Chitas) which covers Chapter 157 usually in the mid-summer months (approx. 19 Tamuz). tanya 157
The Alter Rebbe writes to a disciple who is suffering from "heaviness of the heart" ( Koved HaLev ), a state the Rebbe argues is worse than any physical ailment or even spiritual sin. The central verse anchoring Tanya 157 is from Psalms 100:2: "Ivdu et Hashem b’simcha" — "Serve God with joy." The Alter Rebbe was not ignoring the reality of pain