Gareth Southgate's team face Croatia, who lost the World Cup final to France in Moscow after beating England 2-1 in the Luzhniki Stadium, in Sunday's Group D opener at Wembley with key players such as Luka Modric and Ivan Perisic still prominent for Zlatko Dalic's side.
England have since avenged that World Cup semifinal loss by beating Croatia at Wembley in the UEFA Nations League in November 2018, but Manchester United defender Maguire, who returned to training this week following a month-long ankle injury lay-off, said that he continues to be haunted by the failure to reach the World Cup final in Russia.
With England potentially playing six of seven Euro 2020 games at Wembley this summer, if they top a group which also contains Scotland and the Czech Republic, Maguire added that Southgate's squad can go further than the team which fell short at the semifinal stage at the World Cup.
"The last major tournament, a World Cup semifinal, it ended in disappointment at a stage where I thought we could have really pushed on and gone further in the competition," Maguire told ESPN. "I am still a bit disappointed thinking about that day.
"But we have a great chance in the Euros. We have a young, talented squad with some experience as well, which I'm sure will be key in the tournament.
"I haven't really mapped it out, but I know the group and where we could go and the teams we could avoid and play.
"But honestly, it's down to us and we have to look after ourselves.
"We have a good, talented squad and there is no-one there that we want to avoid. They are all top, top teams, and there are some top players in the Euros, so there are going to be lots of difficult challenges.
"If we are going to go all the way, like we are all hopeful of, we have to beat them."
England will play in front of a crowd of just 22,500 for the opening two group games against Croatia and Scotland, with the figure possibly rising above 40,000 for the final fixture against the Czechs, depending on the potential relaxing of COVID-19 restrictions by the United Kingdom government on Jun 21.
But even though the 90,000-capacity Wembley is unlikely to be full at any stage of the tournament, Maguire says that any number of supporters inside the stadium will be a boost for the players.
"It's not the full World Cup experience, but it's the Euros and I'm sure a half-empty stadium, or should I say half-full stadium, will seem a lot better than what we have played in [last season]," Maguire said.
"The sooner we can get fans back into the stadium the better. Every footballer I speak to says the same -- we miss the fans, they are a big part of the game and they create the atmosphere.
"We feel it on the pitch as well. It won't be the same without a full stadium, but a half-full one is something we are really pleased about."