Hodgson stood squarely behind Hart on Thursday when naming his squad for England's World Cup qualifiers at home to Montenegro and Poland, saying he had faith in the 26-year-old.
Hart performed poorly for City against Bayern Munich in their group game on Wednesday, allowing well-hit but hardly unstoppable shots by Franck Ribery and Arjen Robben into his net in a 3-1 loss.
Television commentator Gary Neville, one of Hodgson's coaching team, said Hart would be "disappointed" after conceding two poor goals but the England coach was quick to defend his keeper.
"I am not blind to the situation, I do realise it is not a good moment for Joe," Hodgson told a news conference.
"He is a proud man and a very good goalkeeper and I am sure when he is criticised he is unhappy.
"I have great faith in Joe and have no doubt he will come through these two games and we'll get the results we need and he'll put one bad game behind him.
Uncapped Fraser Forster's performance for Celtic against Barcelona in midweek was in marked contrast to Hart's but Hodgson said he would have to bide his time.
"Apparently (Hart) went through a bad period last night. But we have let in three goals in eight games so it will take a lot more than one bad game from any player to start suggesting he needs to be replaced, especially with our situation," he said.
"We need experience and need players who are tried and tested and playing regularly at the top level. Clearly looking at that criteria he's our number one.
"It would be a mistake to suggest Fraser Forster at this moment in time should be given the responsibility in these two vitally important games," he added.
Hart's form will cause jitters, however, as England can ill afford any slip-ups in their remaining qualifiers.
He was also to blame for one of Scotland's goals in England's 3-2 victory in a friendly in August and was culpable for Poland's equaliser in a qualifier in October.
There have been several off-days for his club too, particularly in a defeat by Southampton last season when he allowed a weak shot to creep in at his near post and against Cardiff City this season when he failed to reach a cross.
"Maybe it's a bit easier to criticise a goalkeeper for what you think is a mistake rather than a midfielder whose poor play provoked a goal chance a few seconds earlier," said Hodgson, whose other goalkeeping option along with Forster is Norwich City's John Ruddy.
Strikers Wayne Rooney and Daniel Sturridge return to the squad after injuries ruled them out of England's last qualifiers against Moldova and Ukraine.
England are one point ahead of Ukraine and Montenegro in Group H with three games left to play.
(Reporting by Martyn Herman; Editing by Clare Fallon)
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