A last-minute Ollie Watkins strike saw England come from behind to beat the Netherlands 2-1 in Dortmund on Wednesday night to set up back-to-back Euros finals.
Rice admitted fault for allowing Xavi Simons to fire the Dutch ahead early on, but a contentious Harry Kane spot-kick drew England level, before Watkins struck.
At Wembley in 2021 it was ultimately Italy who were left celebrating after beating Gareth Southgate's side on penalties.
Rice, who started that game and has played every minute of England's Euro 2024 campaign in Germany, knows there is a similar challenge to overcome this time but wants to go one better.
Asked if there was a sense of unfinished business from Euro 2020, Rice replied: "Yes, definitely. Look, seeing Italy lift that trophy will haunt me forever.
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