Celtic's hopes of making it to the group stage of the competition were dealt a blow by the result of the game.
Jota's second-half goal brought the Scottish champion level after Christopher Nkunku had put the Red Bulls ahead.
Their good work was undone when Hart gave the ball to Szoboszlai, who set up Silva to score.
The German side leapfrogged Celtic in Group F thanks to a brilliant move by the Portuguese forward, with the Socceroos still looking for their first win of the season.
Nkunku was denied a goal by the video assistant referee before the Frenchman, who has been linked with a move toChelsea in January, scored the winner.
Szoboszlai hit a post after a great move involving Nkunku and then his goal was ruled out after the referee reviewed footage of Silva blocking Hart's view.
Hart immediately passed the ball to Szoboszlai, and Silva made him pay, as Celtic rued not taking advantage of the chance that came their way.
Nkunku pinged a fantastic pass across to Simakan, who in turn provided the assist.
Celtic had played well until Hart made a mistake. Jota's goal was a well- worked one, as Reo Hatate picked off a slack pass and fed Kyogo Furuhashi, who slid the ball home.
Before that point, Kyogo had a shot that was just past a post, as well as a shot that was just past a post by Hatate.
It was the same story as the defeat by Real Madrid and the draw with Shakhtar Donetsk, where Celtic were not clinical enough in front of goal.
Celtic can return to Glasgow with their heads held high but also with a lot of regrets. They pressed and picked off slack passes despite missing their first-choice centre-backs.
Jota's goal was well worked and came as a result of good pressure in the middle of the field.
The team's inexperience is costing them. In the big moments, only two of the nine starters have played a lot of minutes in the competition.
They are punished for their mistakes when they are wasteful in front of the goal. Two of the mistakes which led to goals were committed by players with elite level experience.
The first came from McGregor's heavy touch on the edge of his own box, while the second came from Hart's inexplicable pass to Szoboszlai.
The quality of the opposition is important. Nkunku, Szoboszlai, and Sim on the right were threats.
The Germans will come to Glasgow next week with confidence after a poor start to the season, and will want to put Celtic out of the equation for second place in the group.
On Sunday, Celtic are away to St Johnstone, and on Tuesday, they are at home against Leipzig.
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