The Manchester City man has been England's undisputed first-choice goalkeeper throughout Hodgson's 16-month tenure, but he is facing questions over his hold on the number one jersey for the first time.
After a mixed 2012-13 campaign, Hart was at fault for Scotland's opening goal in their 3-2 loss to England earlier this month and was also criticised following City's 3-2 defeat at Cardiff City on Sunday.
Hodgson, however, believes the 26-year-old will benefit from his time with England, citing the example of Wayne Rooney, who joined up with the national squad for the Scotland friendly despite a pre-season dogged by injuries and speculation about his Manchester United future.
"It would take more than a couple of games before we lose faith in a guy who has proved himself to be England's number one over a long period," Hodgson told reporters at Wembley Stadium.
"I'm rather hoping that Joe will use the England time together to get his confidence restored, and he'll be working with people who believe in him.
"Certainly Wayne was happy to be part of the Scotland game and happy to use that time to dispel a few doubts about him.
"I can only hope that Joe will do the same, but I will be vociferous in my defence of him because I think he deserves it."
Rooney's future appears slightly less muddied after his determined showing in United's 0-0 draw with Chelsea on Monday prompted visiting coach Jose Mourinho to suggest he may have decided to stay at Old Trafford.
The former Everton player has been the subject of two unsuccessful bids from Chelsea in recent weeks, but Hodgson said he was not surprised that Rooney had managed to put the speculation to the back of his mind.
"I think he's a strong character. I think he's an out-and-out footballer. I think he loves the field, he loves to play," Hodgson said.
"First on, last off. You drag him from the field, you tell him: 'Don't kick so many balls, you've got a game tomorrow, save your legs.' He's that type of player."
Hodgson was speaking after announcing his squad for England's World Cup qualifiers at home to Moldova and away to Ukraine next month.
He handed first call-ups to Everton teenager Ross Barkley and Tottenham Hotspur winger Andros Townsend, as well as recalling Liverpool's Raheem Sterling, and said that all three would bring something new to the squad.
"Barkley is a player more in the realm of Jack Wilshere and (Alex) Oxlade-Chamberlain, just to name two -- Theo Walcott, if you want a third -- who are capable of receiving balls in tight areas and going past people," Hodgson said.
"They bring a dimension that we're interested in and we think they have a great future."
Hodgson also said that Arsenal manager Arsene Wenger had not expressed concerns about the selection of midfielder Wilshere, who has been hindered by ankle problems.
The 21-year-old was on the receiving end of some rough treatment in Arsenal's Champions League victory over Fenerbahce on Monday, and Wenger has already called for him to be rested for the Moldova game.
"I speak to Arsene quite regularly and he's said nothing to me about it," Hodgson said.
"In the conversations I've had, he fully realises that Jack Wilshere is an integral and important part of the England team. We play four days apart, and he expects him to play his part for England."
England can be sanctuary for Joe Hart, says Roy Hodgson
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