The 68-year-old returned for a second spell at the club in January, taking over from Vladimir Petkovic.
Lazio ended the campaign in ninth position, missing out on European qualification, with the season also being marred by an ongoing row between the club's fans and officials.
And Reja told Lazio's official radio station Lazio Style Radio on Thursday that he would not be continuing in his role.
"When we said goodbye at the end of the season, the president (Claudio Lotito) had renewed confidence and trust and proposed to continue the relationship," he said.
"I told him I had a feeling that my cycle had ended, it was right to change.
"It is right that Lazio changes coach to provide new ideas, new enthusiasm.
"We cannot continue this critical situation with the environment, it is not good - we need to find the right system to rediscover the enthusiasm.
"I believe it is right to change to give a new enthusiasm to the team and to the fans.
"The players need the support of the people, something that we have lacked without our fans. With a bit more perhaps we could have done it.
"We must recreate the right excitement - people must be closer to the team, the club has to repair its relations with the fans, or in how they expose themselves, or in the way that they operate.
"The experience in Rome has been the toughest of my life."
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