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And that is why he chose Manchester United striker Marcus Rashford ahead of Leicester midfielder Danny Drinkwater.
Hodgson, speaking before Thursday's final friendly against Portugal at Wembley, said his selection was "tilted towards an offensive approach".
He added: "It became a question of do I take the extra attacker or midfielder? That's how Rashford came about."
Hodgson's side begin their Group B campaign in France against Russia on 11 June, before meeting Wales on 16 June and Slovakia on 20 June.
Eighteen-year-old Rashford's rapid rise into the England squad, scoring on his debut against Australia last week, was described as "incredible for his age" by captain Wayne Rooney.
And Hodgson added: "Rashford's had that fantastic end to the season and it will be very interesting to see in a squad of 23 whether he can bring those qualities at a higher level."
Hodgson, 68, has been criticised for picking just three recognised central defenders but he is confident England will be solid in defence.
"We believe defending is very much a team job and we can't just rely on a back four and a goalkeeper," he said.
"We need great mobility and great running power to defend in that way. With this squad they've got the ability to give us that.
"Often in a tournament the players that get injured or suffer a lack of form are the guys at the cutting edge, the guys who make the difference or score the goals."
He added he was happy he had so many good players to put on the field.
"Systems win you nothing and football players win you games," he said. "If they perform anything like they're capable of we'll be a tough team to beat."
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Tozer, 26, spent 2015-16 at Yeovil, who he joined from Northampton.
The Plymouth-born player said: "It has been a bit of a whirlwind with the deal being sorted out so quickly, but I'm delighted to get the deal done and over the line."
Newport manager Warren Feeney said: "He has experience at this level which will be a great benefit for us."
Find all the latest football transfers on our dedicated page.

Peter Whittle, the party's culture spokesman, was selected over deputy chair of UKIP Suzanne Evans.
In a BBC interview he said his priority would be to encourage people to stay in London rather than being forced to leave the city for financial reasons.
He also said he was opposed to the expansion of Heathrow airport.
And Mr Whittle believes people in the City of London would not be concerned if UKIP won, claiming many in the financial sector want to leave the EU.
When Mr Whittle was asked if Ms Evans would have made a stronger candidate than him, he insisted it had been a robust and fair selection process, and he was good friends with Ms Evans.
He denied she was not chosen because of disagreements she had had with party leader Nigel Farage.
Mr Farage said: "Peter has been an asset to UKIP for many years, and I am delighted to learn that the party has elected him as our candidate in the battle to become London Mayor."
Mr Whittle was born in Peckham, grew up in Shooters Hill and has lived and worked in the capital his whole life. He also set up the New Culture Forum think tank.
UKIP also announced Ms Evans would stand as a candidate in the London Assembly elections.
The radio DJ Mike Read will also stand as a candidate for the party in the London Assembly elections.
Tooting MP Sadiq Khan has been selected as Labour's mayoral candidate, the Lib Dems have chosen Caroline Pidgeon, the Green Party has Sian Berry and George Galloway will represent The Respect Party.
The Conservative Party has not yet selected a candidate. The party's Boris Johnson, who was elected as an MP in May's general election, has been mayor since 2008.
Manager Roy Hodgson says his final 23-man England squad for the European Championships is based on attack.
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Defensive midfielder Ben Tozer has joined League Two's Newport County on a one-year deal.
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UKIP has chosen its candidate to stand for London Mayor at next year's election.