The 26-year-old has returned to Argentinian side Velez Sarsfield, the club where he started his career after spending four years in Serie A.
Zarate only made five appearances for Lazio in all competitions last season and he delivered a parting shot at Lotito upon his exit.
"Why have I come home? I needed to feel important, to feel liked - the last days were very hard for me," he said.
"In November, I had been training for the last time with the team and already I felt no confidence. I had not played a single minute in 15 games.
"I watched a game and then I went to the bathroom to cry, it's terrible when they don't let you do what you want."
"The blame is on Lotito and a few players, in addition to the coach, it is them who make the decisions.
"The president failed to meet agreements and did want to pay me. He didn't want me in his team but would not let me leave either. Lotito hurts the club and devalues the objectives of Lazio."