The Three Lions reached the last four of the 2018 World Cup but were left deflated as they were knocked out by Croatia in Russia three years ago.
However, Gareth Southgate's side have put that disappointment behind them as they reached the semi-finals of another major tournament following a dominant 4-0 win over Ukraine in Rome.
Only Denmark stand in the way of England and an appearance at the Euro 2020 final and Maguire insists there will be no basking in the squad's achievements so far.
"It is a great feeling. Back-to-back semi-finals is a great achievement - I don't want to be a party pooper but we have another big game coming up," the former Sheffield United defender told BBC Sport.
"We want to go further than we did at the World Cup. It is a great feeling to win here. It shows the big progress we are making and long may the improvement continue."
He continued: "I think it is hard to soak it all in when you have got another big game coming up and you know who you are playing.
"The dressing room will be a great atmosphere tonight but tomorrow when we wake up we will be focused again.
"This group of players aren't settling for a semi-final, we want to go to further."
The Manchester United player scored England's second goal of the night at the start of the second half to settle the nerves with two goals from Harry Kane and one from Jordan Henderson rounding off the scoring.
Kane's first goal came four minutes into the game as he raced onto to Raheem Sterling's pass before prodding the ball home. The Tottenham striker headed home his second on 50 minutes before Jordan Henderson scored from Mason Mount's corner after coming off the bench.
England scored two goals from set-plays and, of his goal, Maguire added: "We spoke before the game that we wanted to be better at attacking set plays.
"It was a great ball from Luke [Shaw] and I got a great connection on it. It is nice to chip in with the goal and the victory."
Ukraine had started to build pressure at the end of the first half but Maguire's goal in the first minute of the second half proved decisive.
"We have great belief in the dressing room. The first half was tough and we obviously got the early goal we wanted," added Maguire.
"They caused us a few problems when they changed things but the second goal settled us down and from then on, we controlled the game really well.
"It was an impressive performance in the end."
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