The Manchester City goalkeeper's error led to Scotland's opening goal on Wednesday night and the England manager admits he will be keeping an eye on the 26-year-old from now on
Hart was at fault for the opening goal of England’s 3-2 victory at Wembley, allowing Scotland captain James Morrison to find the back of the net after failing to keep hold of the ball.
The 26-year-old has been relatively unchallenged for his position having established himself as a first team regular in 2010, though Hodgson has warned he will "be watching him closely" in coming games.
"Joe’s place is as much open to competition as anyone else’s - I can’t give guarantees," he told reporters following the match in celebration of the Football Association's 150th anniversary.
"But I would contest the view he doesn’t have competition. Ben Foster is a good goalkeeper and now we have John Ruddy back [from injury] as well, while Jack Butland has talent.
"I wouldn’t leave Joe out of the next game because he made that mistake but like everyone else, the competition for places is getting stronger."
Hodgson revealed Hart’s personal disappointment at his error in the first meeting between the two sides since 1999 but insisted his country still has belief in his abilities.
He continued: "Joe was gutted. The first thing he said to me at half-time was to apologise for letting in the goal.
"It is not a perfect world. Good players make mistakes. People you wouldn’t dream of missing a goal chance miss tap-ins and keepers who are very good throw them in.
"The important thing for Joe is to get a good start to the season with Manchester City. We still believe in him."