The 26-year-old fumbled a Franck Ribery effort into the net for Bayern's first goal in the Champions League fixture on Wednesday, before Arjen Robben beat him at his near post for the third.
Those errors have seen the shot-stopper once again in the spotlight ahead of England's crucial World Cup qualifying fixtures against Poland and Montenegro at Wembley, but Hodgson insists he will retain faith in his regular No.1.
"I believe that Joe will shrug this off," the Three Lions boss told reporters. "I'm sure he's not happy with the criticism, I'm sure he's not happy to let in goals he feels he could have stopped.
"As far as I'm concerned, he's never let me or the team down in the time I've worked with him so I have every confidence, every faith in him that he will put it behind him.
"He kept clean sheets against Ukraine and Moldova, so it will take more than one bad game from any player for me to start suggesting that he should be replaced by anyone else.
"Especially at the moment when we need experience. We need players who are tried and tested at this level, who have played regularly at the top level.
"If you look at the goalkeepers we have available that fit that criteria he's clearly No.1."
Hodgson also welcomed the return of strikers Wayne Rooney and Daniel Sturridge to his squad, who missed the most recent qualifiers due to injury, and believes he has an excellent array of attacking options to choose from.
"The more choices I have, the better. I was excited before the last two games. I was watching Sturridge and Rooney and was thinking they were in great form," Hodgson continued.
"There's lots of goals in the sense they can create goals through their individual ability their individual brilliance.
"Unluckily, we lost them so hopefully this time we won't. [Rickie] Lambert is playing well and [Jermain] Defoe as well."