Wayne Rooney struck the game's only goal from a free kick to maintain the Three Lions' 100% record on the road to France.
Hodgson told BBC Sport after the game: "It was hard work. We played well in the first half without taking our chances and that meant that there was an air of frustration setting in.
"Everyone was aware that when you have played well you have to take at least one chance. Luckily we did that in the second half and it's four wins in a row which is not to be sniffed at."
England's next qualifier is at home to Slovenia on November 15.