The 39-year-old parted company with the Ibrox club on Thursday three years after initially joining on loan from Bournemouth before making the move permanent.
The striker signed a new one-year contract in the summer as a player-coach but admitted he struggled to combine the roles as he managed just two substitute appearances this season.
Defoe scored 32 times for the club despite making just 33 starts.
"Many people were speculating and didn't really understand what was going on," he said.
"I got given a player-coach role but, me being me, I just wanted to focus on playing.
"The player-coach role is something completely different and doesn't get given out too much in football.
"At the beginning it was difficult to find a balance in terms of when do I do a little bit of coaching, and when do I train 100 per cent.
"I had a few conversations with the manager, Stevie [Gerrard] at the time, and we spoke about how difficult it was because I was trying to find time to do coaching while playing and training every day. I did a full pre-season.
"It was really difficult for me because I was so focused on playing. I did everything I did the season before and wasn't really getting an opportunity. It was pretty clear towards the end I wasn't going to play."
Defoe had hoped to win over new Rangers manager Giovanni van Bronckhorst as he looked to recapture the form that saw him feature 20 times and score seven goals in last season's title winning campaign.
"I've still got that mentality to impress the new manager and get in the squad and hopefully get a few games under my belt," he told Sky Sports.
"When you're involved in the season we had before, winning the league and that feeling, the next season you still want to be a part of it because you've still got that buzz. The fans are back in the stadium and Ibrox is an unbelievable place to play football.
"Even at the age of 39 I still wanted to be involved. Towards the end it was affecting me, I was bringing it home and I was a little bit down.
"I had an honest conversation with the club and it was going to be difficult to see where I was going to get my games with the new signings coming in and the club doing well. That was it really."
Defoe thanked the Rangers fans for their backing, admitting their response to his departure left him "overwhelmed".
"I wish I could message everyone back," he said. "Some of the message I've received - it's unbelievable. Overwhelming.
"I look at players like Ally McCoist who have been at the club a lot longer and scored a lot more goals than me, and staff members who have been at the club for 30 years.
"So when I received the messages from Rangers fans it's quite emotional and I wish I could mesasage them all back. I'd just like to thank them all for their support.
"It's not easy to walk away from it, but that's football."