Ukraine must win to reach the last eight while England only require a draw in Donetsk’s Donbass Arena on Tuesday.
Hodgson said: “Our aim is to take the initiative like I thought we did for a very long period against Sweden.
“If you sit back and give the initiative to the opposition then you can’t be surprised when they take it.”
“It will be no easy task against the co-hosts, who need victory to sustain their own hopes of progression and will be backed by fervent and colourful support in the biggest match in Ukraine’s history”
“We will be trying to make sure we take the initiative but Ukraine will be trying to do the [same] and that is what makes this a fascinating game of football.”
England have taken four points from their first two games following the opening 1-1 draw with France and Friday’s stirring 3-2 comeback win against Sweden.
Captain Steven Gerrard insists the team are looking no further than the game against co-hosts Ukraine.
“I am trying to force myself not to even talk about quarter-finals and get involved in it. It would be very disrespectful to the opposition,” said the Liverpool midfielder.
“Ukraine are very dangerous and we have watched tapes of them. Their combination play in the middle and around the box is good.
“If I started talking about quarter-finals and we slipped up, I would never forgive myself. Let’s deal with the quarter-finals and what to expect if we get there and not before.”