England scored just three goals in their Group B campaign and were held to a frustrating 0-0 draw against Slovakia last time out despite enjoying over 60 per cent of possession in Saint-Etienne.
Hodgson knows there will be less space against Iceland than there would have been against Portugal and expects England will need to be patient once again, while showing more creative spark in the final third.
"I fear it [the game with Iceland] won't differ enormously from our group games because Iceland are not an expansive team," he told FA TV.
"Their success has been built on a very solid defensive organisation and incredibly hard work ethic.
"I know the coach very well, he prepares his team in that way so I don't think we'll benefit from lots of space in the game so we'll have to make certain we are aware of that and hope we can keep the kind of domination we've had in the games, keep the control but maybe be a bit more ruthless and have a bit more of a killer instinct in front of goal because our ratio of creating chances and taking chances is not good.
"That needs to be improved and everyone is aware of that. It would be nice if we could start with that on Monday."
England's second-place finish in the group stage means they sit on the same side of the draw as Germany, Spain, Italy and France, but according to Hodgson there is belief within his squad they can compete and reach the latter stages.
He added: "Results are of course what matters and if you don't get the results you've got to be very disappointed and very unhappy, especially at tournament level.
"We were the favourites to win the group, I think we were deservedly favourites and I honestly believe we did enough to win the group, but we didn't because the performances were matched by the results.
"As a result we have to accept second place and possibly go into, on paper, a harder part of the draw.
"But the mood in the camp is good because the players honestly believe they are a good team and they are capable of beating any team in the tournament on their day."