England's friendly defeat to Germany on Wednesday night was marred by fans booing the German national anthem and singing distasteful songs.
Football Association chairman Greg Clarke described the chanting in Dortmund as "inappropriate, disrespectful and disappointing".
The incidents came on the same day a terror attack in London which left four pedestrians and a police officer dead.
The FA is planning a number of tributes to the casualties, with black armbands, a minute's silence, a reef-laying ceremony and the Wembley arch being coloured red and white throughout the game - which will also be attended by a number of distinguished guests.
And Dier, set to pick up his 17th cap in the game, wants supporters to show they can be portrayed in a positive light after such a turbulent week.
"In general, the fans have been fantastic with us wherever we go," he said.
"The support they give us is always amazing. But all we ask is that they support us in the right way and they're respectful.
"Because of the dreadful things that happened in London we just hope the fans are very respectful of that and us as players we're going to respect everything in the right way and we're going to do everything to honour the people who passed away this week."
The 23-year-old also revealed his first thoughts on hearing the news of the attack in Westminster was to call home from Germany and speak to his mother - who works close to the scene.
"It's horrible," he said when asked how the attack affected him.
"You never want to see things like that, especially where you live. First thing I did was ring my mum because she works not too far away from there. It's not very nice."
Dier was in the England side which played France in November 2015, just days after an attack on the French capital.
It was an emotional night for all involved and one that has stayed with the Tottenham man ever since.
Asked about football's ability to unite, Dier added: "I think it's massive.
"I was at the France game after (the) Paris (attack) and I thought that was an amazing show of unity. It was quite emotional to be a part of.
"I think it showed how football can bring everyone together. Hopefully on Sunday we can do the same."