Tommy did experience peace and happiness for a brief period of his life, and that is his tragedy. It wasn't that he was never able to feel it; rather, he *did* feel it, but the life he so hated, and wanted to escape, stripped that happiness and peace away from him when Grace died.
Before Grace, he used to hear the sound of shovels against the wall; she was the only one who silenced his trauma. When he was with her, he could sleep without needing drugs. We saw his vulnerable and soft side with her.
He laughed, and he wanted to change for the better and have a better life for himself and his family.
The change he underwent after her death is profound and undeniable. The hallucinations returned, even more intense than before, and he no longer wanted silence in his mind, because he had to live with his own demons. He became addicted to alcohol, opiates, sex, and power, to anything that might, for a moment, fill the void she left behind, but by Season 5, nothing worked anymore.
All his relationships were transactional; he had no emotional connection with anyone.
He was colder and more calculating than before, even quite cruel, and he no longer showed his softer side or vulnerability to anyone, because that part of him had died when she died.
In Season 3, at their wedding, Tommy toasts to "Peace", and in Season 4, during the family meeting, everyone toasts to peace, and Tommy is the only one who refuses to drink. Why? Because toasting to peace without Grace felt like a mockery.
Steven Knight did not write a man incapable of feeling love or happiness; rather, he wrote a man who found absolute happiness in one specific woman, only to have life tear it away from him.
To say that Tommy was never happy completely negates the beautiful, tragic depth of his character. Grace was no mere fleeting fancy; with her, Thomas Shelby felt secure in his own mind for the only time in his life. And, as we see right up to the final film, he spent the rest of his days haunted by the ghost of the only peace he ever knew.
That is why he feels that:
"Once i nearly got fucking everything"