England reached the World Cup semi-final for the first time since 1990 in Russia this summer.
And Dier believes Gareth Southgate’s side have a new found respect, but the idea is to retain that and show the world just how good they can be.
England are in action for the first time since losing to Belgium in the third place play off on Saturday night when they face Spain in the Nations League.
“We’re a more respected team now, after the World Cup, but the hardest thing now is to maintain that respect,” the Tottenham midfielder told BBC Radio 5Live.
“There’s a a real stability at the moment. I think the manager wants that in the squad, stability and for everyone to feel like they’re part of something.
“That being the case we’re eager to build something. Even though our World Cup was so positive we still feel like we need to prove ourselves against the very best teams.
“Spain had a difficult World Cup but they’re still one of the best footballing nations and we want to compete against the best and beat the best.”
Dier has a reputation for being one of the squad’s more clear-minded thinkers, rated by Southgate as tactically astute and with a continental grounding from his formative years in Portugal.
It is, then, something of a surprise to find out he is still coming to terms with the impact of England’s campaign.
“I don’t even know if it has sunk in yet to be honest,” he said.
“Football moves so fast, it wasn’t long after the Premier League had started again and now we’re four games in and back on international duty.
“It’s kind of crazy. Being with England again and with the atmosphere there will be at the next two games, the first time playing in England since the World Cup.
“I’m sure leading up to those games we’ll really feel the effect it had. During the World Cup it was difficult for us to understand what things were like back home, hopefully we can feel a bit of that on Saturday and on Tuesday (against Switzerland) as well.”
Southgate has named a squad similar to that which went to Russia but returns for Joe Gomez, Luke Shaw, James Tarkowski and Alex McCarthy.
And the Southampton goalkeeper is keen to impress and push himself up the order.
There are four goalkeepers in the squad after Marcus Bettinelli was called up to join Jordan Pickford, Jack Butland and McCarthy.
But the former Reading man is taking it in his stride.
“I wouldn’t say it puts more pressure on me,” the Saints goalkeeper said of Bettinelli swelling the goalkeeping ranks on Tuesday.
“I think, at the end of the day, I sort of concentrate on what I’ve got to do.
“Obviously I’ve been called up for a reason and there’s now four of us here, but it’s a time for me to go out there and prove what I can do.
“We’re away for seven or eight days, so it’s enough time to sort of show him what I can do.
“And at the end of the day, I want to give him a decision to make.
“Obviously it’s an unbelievable feeling to be back here.
“I’ve been in two squads before but that was quite a while ago, so obviously after the World Cup and everything that has gone on it’s been a positive for English football.
“It’s nice to be back involved and a part of it.”