The Manchester City No.1 had a torrid time against the home side's talisman Zlatan Ibrahimovic, who netted four times including a 35-yard free kick and a 30-yard bicycle kick with Hart at fault for both.
Despite the 25-year-old's disappointing display, the 65-year-old boss showed his support for the keeper, stating England will have "a lot of success" with him between the posts.
"These things happen. I think the third goal got a slight deflection, and it was a shot from distance where we wouldn't normally think of conceding a goal," he told reporters.
"The fourth one, he got a very unpleasant bounce. The ball actually really pitched up and he couldn't get the purchase on his header, and it led of course to Zlatan scoring his acrobatic goal."
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For the fourth, Hart raced from his line in the 90th minute to deal with a long ball, but could not get a clean connection with a headed clearance, and PSG striker fashioned a majestic overheadkick from distance to seal the victory.
However, Hodsgon is still confident in his No.1 goalkeeper, suggesting a dip in form is simply part and parcel of any footballer's life - and maintained Hart will recover and lead England on to better days.
He continued: "We're not bothered about Joe Hart, and we think for the future, going forward, he's a very good goalkeeper and we will have a lot of success with him in the goal and if tonight it wasn't maybe one of his absolute best days, this happens in football."