The former Spurs captain left for Los Angeles midway through last season.
He told Le Parisien: "It was a combination of several factors: the team was lacking results and the coach (Antonio Conte), was under pressure, was losing patience. Therefore, the group dynamic was negative.
"Tottenham were coming to the end of a cycle, and so was I. I knew that Tottenham wanted to recruit younger players, especially in my position. Summer was approaching and I was no longer part of the plans.
"When the championship resumed, in August 2023, the coach (Postecoglou) informed me that I would no longer enter the field, that I would only be a training player. I was pushed aside, I had become transparent."
Lloris also said: "Those eight months without playing were complicated.
"Since I've been playing football and I started at the age of six I've been thinking about the upcoming match, planning for the next goal.
"When all this collapses, we no longer know how to make sense of physical effort: why hurt ourselves? Why push yourself to come back?
"However, I was not unhappy. I took the opportunity to spend more time with my family and it did me good.
"I was able to celebrate my father's 70th birthday and go see my brother play in Le Havre, against PSG. It would have been impossible if I had been on a team sheet at Tottenham.
"One day, I know, football will stop for me. I will perhaps miss the adrenaline, because it is a drug, but I am not afraid of this 'little death' as they call it in the sporting world. There is an afterlife, and I can't wait to know it too."