The Three Lions skipper struck the winner with a second-half free kick as Hodgson's men squeezed past the 10 men of Estonia, but the Manchester United captain spurned a number of chances to add to his goal tally.
"It was a good free kick from Wayne, but it was a frustrating night for him," he told ITV Sport.
"He had a lot of the ball and a lot of chances, I think he'd have been bit disappointed if he'd not have scored. But he scored the winner and we go away with three more points.
"We played well in the first half, we played some excellent football without taking our chances and that meant that there was an air of frustration setting in and an air of pressure going out in the second half."
The victory means England have now won all three of their Euro 2016 qualifying games.