Hodgson led the U21s to a 6-0 drubbing of their Scotland counterparts at Bramall Lane on Tuesday night, with Stuart Pearce having been sacked from the role following a disappointing European Championship in Israel.
But Hodgson was keen to stress he will not be combining the roles in future as he prepared to take charge of England for their friendly against Scotland at Wembley on Wednesday.
"I don't think it's feasible," he said. "A lot of the time there is an overlap, and furthermore, I don't think it's right.
"These players need someone who is going to be really concentrating on them and following them.
"I will see some of the players. When I go around looking for seniors, I will see some of these.
"But we need a manager who is going to follow them even if they are playing reserve team football.
"They need someone who is going to carry on the work that Stuart has started which we have tried to carry on here in this brief spell we have had."