Almost since the 2010 World Cup, Hart has seemed like the one player England cannot do without. Yet mistakes that have crept into his game at Manchester City have spilled onto the international scene as well.
On Wednesday night, there were a couple of minor errors, in addition to two major ones, the last of which allowed Zlatan Ibrahimovic to score his jaw-dropping fourth goal in Sweden's 4-2 friendly win. "We are not bothered about Joe Hart," said Hodgson.
"He is a very good goalkeeper. We think we will have a lot of success with him in the goal even if tonight it wasn't maybe one of his best days, this happens in football."
Indeed, Hodgson was pretty upbeat despite the loss of his unbeaten record as England boss in open play - his only previous defeat coming on penalties at Euro 2012.
First-half goals from Danny Welbeck and Steven Caulker in response to Ibrahimovic's opener appeared to have set England on course for yet another victory over the Scandinavians, with 17-year-old Raheem Sterling amongst those to impress.
"Raheem has to be very happy," said Hodgson. "He had a difficult start. The first challenge on him was a very fierce one. It put him on the ground and winded him.
"But he came through that and got better and better. Towards the end he tired a little as one would expect but I have to be satisfied with what he did. He is not even 18, so it bodes well."
Unfortunately, they reckoned without Ibrahimovic, the man derided so often by English audiences, becoming the first player in history to score four times against them. And the coup-de-grace was that quite amazing fourth, an overhead kick from fully 25 yards which England skipper Steven Gerrard said was the best goal he had ever seen.
Zlatan Ibrahimovic ripped off his shirt and sprinted along the touchline to celebrate the remarkable late goal.
"Even if it was a friendly I had to show my happiness and give it back to the crowd," he said.
"What went through me then it's hard to describe. I enjoyed it very much."
Hart came out of his area to clear a long pass but only succeeded in heading the ball up in the air and Ibrahimovic launched into an acrobatic overhead kick to send it sailing into an unguarded net.
Asked if it was his best international strike, the Sweden captain replied: "No - but it's the one I've enjoyed most.
"Hart was a long way out and I was just trying to get it into the goal. I was on the ground when it was on the way in.
"I saw a defender sliding in to try to get rid of it and I wanted to scream 'No' but the ball went in."
The Paris St Germain marksman is up to third in Sweden's all-time scoring chart after taking his tally to 39 goals in 85 internationals.
Having often struggled against their teams in European competition, Ibrahimovic has never enjoyed the best of relationships with the English fans and media but he certainly made new friends at the new Friends Arena in Stockholm.
"That's the way it is with the English," he said. "If you score against them you're a good player, if you don't score against them you're not a good player.
"I remember Lionel Messi before the 2009 Champions League final for Barcelona ... then he scored against Manchester United and suddenly he was the best player in the world.
"Maybe now they'll say something like that about me," added the 31-year-old.
The Swede is now looking forward to scoring many more goals at the Friends Arena.
"It feels like a coliseum, this arena is going to give us a lot of points in the future," he said.