The now 29-year-old made the decision to leave the Three Lions' camp at the 2022 World Cup in Qatar to return home for personal reasons. White then made himself unavailable for selection for the rest of Southgate's reign.
He has since returned to the fold under Thomas Tuchel, making his return to a chorus of boos in the game against Ukraine back in March.
White has also been called up to the England squad for their upcoming UEFA Nations League games against Croatia and Spain.
Asked on BBC Radio 5 live about his decision to walk away in 2022, White said: "I think obviously people don't know the full story, because I (have) never said anything and I won't put anyone under the bus or share any of that.
"I think that is probably the best way.
"It's been amazing (though), obviously a bit tricky and not straightforward, but it is amazing to be here now."
White is now 29 and asked if he would have done anything differently in hindsight, he added: "No, I don't think I would.
"Obviously, I was a bit younger, I am a bit older now.
"I think as a person I am quite real and I think I made the decision that I would probably continue to make.
"So, one that I am not happy about, but obviously it happened and (it is) time to move on."