Sterling came off the bench with 36 minutes left in Tallinn, winning the free-kick that saw Wayne Rooney score the winner in England's 1-0 triumph over Estonia in Euro 2016 qualifying.
The 19-year-old did not start, with Hodgson claiming Sterling had approached him on Saturday, claiming he was not mentally ready to play.
"People don't like it when you simplistically tell the truth. We were training at The Grove doing a light session but some work in how we wanted to play the game tactically," Hodgson said.
"Just before we started, Raheem had done the warm up and he came to me and said 'look I really am feeling a bit tired, I'm not in my best form at the moment because I am feeling a bit tired'.
'So I said best thing is Adam Lallana starts the game and you rest and I have got you to bring on from the bench, simple as that."
Hodgson said Sterling could be mentally jaded after a tough start to the Premier League season with Liverpool, having started six of seven matches for the Anfield outfit in England's top division.
"There is an awful lot going on in his head. Perhaps it's quite simply the season hasn't started quite as well for Liverpool as they wanted," the 67-year-old said.
"He's player who's always in the focus and spotlight for England and Liverpool, maybe that's had some effect. But I don't know, it's a theory.
"In mitigation of a young player, when you break into a team like Liverpool and you have a fantastic season, then you go to the World Cup and you do well and people regard you as one of the few who lived up to his reputation.
"Then you come back and you're still only 19 years of age, there are a lot of other things that play a part in people's make up. It isn't quite as simple as the training you're doing maybe taking some juice from your legs."
