Gareth Southgate's side booked their place in the last 16 of the tournament on Sunday by crushing Panama 6-1 in Nizhny Novgorod.
England end their Group G campaign against fellow qualifiers Belgium on Thursday, with the two nations knowing the winners in Kaliningrad will finish top of the table.
And Carragher - who was in England's squads for the 2006 and 2010 World Cups - believes the fixture offers the perfect opportunity to make a statement in Russia.
"It might be that finishing below Belgium creates what appears to be a more 'favourable' draw, avoiding Brazil or Germany in the last eight. Equally, the group's top side may avoid a tricky last-16 meeting with Senegal, who include Sadio Mane and Ismaila Sarr, or impressive Colombia.
"What looks more desirable does not always work that way – have we forgotten the pre-match optimism before Iceland two years ago?
"England must plot their route by trying to win against Belgium rather than half-heartedly accepting a defeat, or waiting to see if the fair-play table decides the placing.
"I want to see England adopt the mentality they will need against tougher opponents in the knockout stage. How often have we seen the side settle into a holding pattern where extra-time or penalties loom?
"Even if a draw is working to England’s advantage, there is a chance to experiment with more tactical drills with regards protecting a result. Imagine the belief in the players if their courage secures a positive outcome again Belgium. Confidence will soar."
England will be pitted against Colombia, Japan or Senegal in the next round, with heavyweights Germany and Brazil looming large as potential opponents in the quarter-finals.
Yet Carragher feels the previous successes enjoyed by Premier League clubs in Europe - with his old team Liverpool reaching the Champions League final in the 2017-18 season - provides Southgate and his players with the blueprint to succeed when cast in the role of underdogs.
"Unlike so many of our club teams in the Champions League, England have failed to show they can upset the odds when meeting higher-ranked sides," he continued.
"For all the encouragement correctly taken from the first two World Cup games this season, that is the next albatross for Southgate's side to remove."