Roy Hodgson’s men, in their first outing since being eliminated from the World Cup finals at the group stage, edged a forgettable encounter at Wembley Stadium 1-0 on Wednesday.
Wayne Rooney’s 41st goal for his country, and first since being appointed captain on a permanent basis, saw England over the line.
The Manchester United striker’s well-struck penalty was, however, one of just two shots on target from the Three Lions as they once again struggled for creativity and an attacking spark.
Hart, though, claims Hodgson’s side will head into their first European qualifier against Switzerland on Monday in confident mood.
He told Sky Sports: “I thought we were good first half. A little bit slow at the start of the second half, but we dominated the game.
“We’d have liked to have scored more, but a win is a win. It’s a new campaign, a new start for us and we go to Switzerland confident.”
Hart also feels that a positive result will help to start moving England away from their struggles in Brazil and towards their next target – Euro 2016.
The Manchester City goalkeeper added: “We are going to learn from our mistakes, of course, but that’s in the past now.
“The only thing we can do for the good of ourselves and for the good of English football is to move on, be positive and set our sights on France.”