The Three Lions only mustered one shot on target against France - the goal scored by defender Joleon Lescott from a Steven Gerrard set piece.
And former Inter Milan boss Hodgson is aware an improvement needs to be made if England are to qualify from Group D.
Hodgson told the Press Association: "I was happy with the start. We played quite well, certain aspects of our game were good.
"We must maintain that and, if we are going to win matches, we've got to continue to work hard on the attacking side of the game.
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"We have to try to make certain when we do get these good counter-attacking opportunities that we maximise them and take advantage to the full.
"When we win the ball back and break out, we've got to make certain the last pass, cross or actual finish is very clinical.
"It is hard to get good goal chances at this level of football. You are not going to get many during the course of a game and you have to be very effective when the chances come your way.
"I am not talking about the clear-cut one versus ones with the keeper but the situations where you've got behind the defence and it's a question of making sure the last pass gives someone the chance to score a goal.
"That is something we've been working on consistently."
When asked about whether there would be any changes for the game against the Scandinavians, Hodgson revealed he hadn't yet made his mind up on who he would select.
He said: “I haven’t decided on the team yet. The training session tonight will be important in deciding."
After losing their opening game against Ukraine, Sweden need a result to kickstart their campaign. And with Erik Hamren's side possessing several tall players, Hodgso admitted that he is worried about the threat of set-pieces.
He said: "We all agree in today's football set-pieces are very important and it is rare not to have respect or concern over the quality of the opponents' set-plays.
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"I'm also fortunate we have some good set-play specialists of our own and we scored against France not least thanks to Steven Gerrard's wonderful delivery from a free-kick.
"All you can do is prepare in the best possible way and make it clear to your team what threat the opponents pose.
"France posed a lot of threats from their set-plays and Sweden will be the same."