The Tottenham forward - on as a 71st-minute substitute - headed home from Raheem Sterling's cross in a 4-0 Euro 2016 qualifying win over Lithuania, living up to the hype that had surrounded his expected appearance.
Hodgson, though, says Kane is vying with Wayne Rooney for a starting berth, and he is not prepared to change his system to include both.
"It's good Harry gets his chance and grabs it with both hands - it adds that bit of magic to the evening," Hodgson told BBC Radio 5 Live.
"In this way of playing, he competes with Wayne Rooney. To get him in the team we would have to change our way of playing.
"We can do that but the players are suited to the way we're playing at the moment.
"We've got so many good players I feel whoever I put in will do a good job. Everyone's trying to be a good unit."
Rooney, Danny Welbeck and Sterling - scoring his first international goal - had all found the net before Kane stole the headlines.
"You can only beat what's in front of you," added Hodgson. "We had to work hard to wear them down in the first half and we got our reward in the second half when they tired.
"Our major test will be when we get to France [for the finals] and I'm convinced we'll get there. We've got a year and bit to work with them and this team are so young."
