Sturridge, who scored 21 Premier League goals for Liverpool in 2013-14, found the net with a superb individual strike at Wembley on Friday.
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"There are obviously certain players who have their spots nailed down, but in my mind I haven’t and I am working hard every day to show what I can do," he told the Daily Mail.
"For me there are no guarantees in football and I will just work hard and not worry about what team the manager will pick.
"I will focus on what I can do for the team and leave the decisions to the boss because that is what he does.
"I haven’t thought about my goal against Peru - it’s gone now. I’m not revelling in it, I’m not worrying about it. It’s about the team, it’s not just about myself."
Concerns over the fitness of Wayne Rooney have led to suggestions that the Manchester United man should be dropped in favour of giving the in-form Sturridge a free role to lead the attack in Brazil.
But the former Chelsea forward refused to be drawn on his partnership with Rooney, admitting he feels no extra burden given the recent poor showings from the 28-year-old.
"I try not to think about the pressure, it’s about the team, not just myself and Wayne Rooney," he added.
"We have a great squad and whatever happens out there in Brazil we just want to put in the performances that we can be proud of."
England arrived in Miami late on Sunday night, with Hodgson's charges set to face Ecuador on Wednesday as their preparations continue.