Lampard's 13-year spell at Stamford Bridge came to an end at the conclusion of last season when his deal with the London club expired.
The 36-year-old former England international then agreed a move to New York City, who start life as an MLS franchise in 2015, before being loaned to Premier League champions Manchester City, who have a partnership with New York.
"I would have obviously stayed if Chelsea had offered me another year," he told The Sun. "There was no reason for me to leave.
"Yes, I wanted to play a bit more regularly but I'm not stupid.
"If Chelsea had given me a new contract it would have been mad not to take it at the time.
"It wasn't that I didn't think I could still do it. If I felt like that I wouldn't have gone to City on loan.
"I had a chat with Jose Mourinho and both he and the club were always great with me. The decision was made – and I don't know who made it."
He added: "Jose was brilliant about it. I didn't walk out with any bad feelings towards him or the club.
"I knew things were coming to a head but I'm realistic and, in football, I move on quite quickly.
"I also felt like I didn't want to be a player who faded away – with that being the last memory people had of me.
"So maybe it was the right time. Maybe it was right that the club took it out of my hands.
"What I really want now is to make a really positive impact in my time at Manchester City and then again in the next stage of my career."
