The 19-year-old Sterling asked to "sit out" of the Euro 2016 qualifying victory in Estonia on Sunday before coming off the bench in the second half to earn the free kick from which Wayne Rooney scored to secure a 1-0 win.
Hodgson indicated that Liverpool should also shoulder the responsibility for resting Sterling.
"He (Sterling) said, 'I'm feeling tired, I'd rather sit this one out'," Hodgson, a former Liverpool manager, said.
"It's unfair if all the expectations to give the player a little bit of a break fall on me,” he added.
"He broke into the Liverpool team, had a fantastic season and then went to the World Cup. He is only a 19-year-old. It is not as simple as the training you are having may be taking a bit of juice from your legs,” Hodgson said.
"There is an awful lot going on in your head as well, so perhaps it is quite simply that the season has not started as well for Liverpool, and he is in the spotlight for England and Liverpool. Maybe that has had some effect. I don't know. It's a theory,” he added.
"Having Sterling up your sleeve can be a very, very important factor. There's nothing wrong with him. I'm sure when he goes back to Liverpool he'll be fine" the 67-year-old said.
Hodgson also questioned Liverpool manager Brendan Rodgers' claim that some players need two days to recover after matches and indicated it would not be standard procedure for England.
"Raheem might say it is something that is becoming ingrained in him and that he felt the need to talk about being tired more than normal," said Hodgson.
"I don't think there's medical evidence to support the 'two-day recovery',” he added.

The role of England coach has continually required diplomacy between the national side and Premier League clubs, with Hodgson's predecessors having clashed with former Manchester United manager Alex Ferguson and Arsenal's Arsene Wenger over the availability of their players.
Sterling was rested by Rodgers in a league match against Aston Villa in September but played 120 minutes in a penalty shootout win over Middlesbrough in the League Cup.
He played only the first half in England's 5-0 win over San Marino at Wembley on Thursday before being substituted for Anfield team mate Adam Lallana.
The teenager faced a backlash in British media and from England fans on Monday morning for not being able to handle the rigours of two matches in four days for his country after starting most of Liverpool's games this season.
Hodgson later attempted to play down his reluctance to play, though, in a bid to avoid falling out with Rodgers.
"To be fair to the lad, I had a decision to make because Lallana was so good in the second half against San Marino," the England manager said.
"It was simple one. When he suggested he wasn't 100 percent in terms of fitness and recovery, it would have been foolish to leave a player like Lallana, who is raring to go, out of the team,” he added.

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