The Manchester United teenager, who scored on his debut in the 2-1 win over Australia last week, was one of five strikers named in Hodgson's 23-man squad to take to France this month.
Former England captain Alan Shearer was critical of Hodgson's decision to leave out Leicester City midfielder Drinkwater, accusing him of favouring reputation over form by selecting Jack Wilshere and Jordan Henderson despite their injury problems this season.
But Hodgson explained his rationale at a media conference on Wednesday.
"He was a tough one to leave out," Hodgson said of Drinkwater.
"As far as we are concerned if you look back over the two years we have been working together, Danny was very much the last man in, in that respect.
"It simply became a question of do I take the extra attacker or midfielder? That's how Rashford came about. He'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.
"It certainly was never going to be 'if we put Rashford in for this game and he does well, we'll take him'. For us it's always been the balance of the squad rather than X v Y who play in the same position.
"The balance is good, if anything tilted towards an offensive approach. We believe defending is very much a team job and we can't just rely on a back four and a goalkeeper.
"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.
"I'm comfortable that, whatever way we want to play, we'll be covered. Systems win you nothing. Football players win you games."
England face Portugal at Wembley on Thursday in their final warm-up friendly before the Euros, and Hodgson has promised to field a strong side, though Ryan Bertrand is set to be rested after picking up a knock.
"I don't need to try anything out any more but I'm not prepared to say the XI who start tomorrow will start against Russia [in the first group game]," he added.
"I don't want to commit myself to a team against Russia in 10 days' time. It will be a strong team against Portugal, Wayne Rooney will be the captain and will play."