Hart's place in the Manchester City side has come in to question after he cost his team a point in their defeat at Cardiff last weekend by flapping at a cross that led to the Welsh side's second goal.
The mistake came two weeks after Hart's blunder allowed Scotland to take the lead against the Three Lions at Wembley.
The 26-year-old struggled for form at times last season during City's failed bid to retain their Barclays Premier League title.
But despite the criticism, Hodgson insists Hart is still very much his first-choice goalkeeper, and backed the former Shrewsbury stopper to get through his bad patch.
"I have every faith in Joe Hart," the England manager said after selecting Hart in his 27-man squad for the upcoming qualifiers against Moldova and Ukraine.
"When I took this job I thought I had a top-class goalkeeper to work with in Joe and 16 months later I still feel I have a top-class goalkeeper to work with.
"I fully support him. He is still my number one choice because he is the number one goalkeeper.
"When you do make a mistake you are going to be criticised for it, but if he is going to continue as a top level goalkeeper, and I am sure he will, these are moments he will have to survive.
"We can't deny that when you let goals in that you could have saved unfortunately it does affect your confidence. That's a fact of life, but I am expecting him to come here as full of desire and enthusiasm as he usually does and I think he will play well in both games."
Hart's plight has been helped by the fact that his main challenger for the gloves - Ben Foster - will miss the double-header because of a foot injury. The Manchester City stopper will therefore be a shoo-in for the two qualifiers as back-up goalkeepers John Ruddy and Fraser Forster have just 45 minutes of international experience between them.
Hodgson sprung a few surprises by naming Andros Townsend, Ross Barkley and Raheem Sterling in his squad for the games against Moldova, which takes place a week on Friday - four days before Hodgson's men play Ukraine in Kiev.
Unlike prior to the win over Scotland earlier this month, Hodgson will have a settled and fit Wayne Rooney to count on for the crucial qualifiers.
Rooney made his second appearance of the season for United in Monday night's 0-0 draw against Chelsea. Hodgson, who was at the game, bristled at claims by one reporter at a press conference that the goalless draw was "boring", and insisted he enjoyed watching a fit-again Rooney put in a typically bullish display.
When asked whether he was happy that Rooney's future had been resolved, Hodgson answered: "Yes, of course. I am relieved for him.
"He is an important player, has been a fantastic servant to England for a number of years and he still has the burning ambition to do well for England.
"I was pleased with how Wayne did but I was pleased with the game as well. It was by far and away the best game I have seen all season.
"I thoroughly enjoyed it, I'm sorry you didn't, I'm obviously out of sync."
England will seriously damage their chances of qualification for next year's World Cup if they do not take six points from the upcoming two games.
The Three Lions trail Group H leaders Montenegro by two points while Ukraine's 4-0 victory in Podgorica in June means they are just one point adrift of England as the qualifying campaign enters the home straight.
It is therefore something of a surprise that Hodgson has called up uncapped duo Townsend and Barkley while Sterling, who has one international appearance to his name, is another intriguing inclusion.
The England manager spoke highly of Sterling when he coached the Under-21s prior to their game against Scotland two weeks ago and it appears that he was also impressed by 19-year-old midfielder Barkley, who scored a brilliant goal for Everton on the opening day of the season.
Hodgson insists all three players are not just there to make up the numbers.
"These players have a bright future and they can make an impact," the England manager said.
"Players like these three can make a difference. They can beat people and they are in there on merit really."
England squad for the World Cup qualifiers against Moldova and Ukraine:
Goalkeepers: Forster (Celtic), Hart (Man City), Ruddy (Norwich).
Defenders: Baines (Everton), Cahill (Chelsea), Cole (Chelsea), Jagielka (Everton), Johnson (Liverpool), Jones (Man Utd), Smalling (Man Utd), Walker (Tottenham).
Midfielders: Barkley (Everton), Carrick (Man Utd), Cleverley (Man Utd), Gerrard (Liverpool), Lampard (Chelsea), Milner (Man City), Sterling (Liverpool), Townsend (Tottenham), Walcott (Arsenal), Wilshere (Arsenal).
Forwards: Defoe (Tottenham), Lambert (Southampton), Rooney (Man Utd), Sturridge (Liverpool), Welbeck (Man Utd), Young (Man Utd).