Gareth Southgate's side face Senegal in Sunday's round-of-16 clash at Al Bayt Stadium as they aim to build on reaching the World Cup semifinals in 2018 and last summer's European Championship final.
With two of the bigger nations -- Germany and Belgium -- already on their way home from Qatar after falling short in the group stage, Stones told a news conference: "It is always difficult when you see big teams or big players in teams that don't have the success that you want or don't live up to the expectation of a nation or where they see themselves.
"We don't ever want to fall into that category. So I think that's great motivation for us as a reminder that you never want to take anything for granted or who you are playing against.
"All we can affect is what we are doing, what games we are playing and who we are playing against, giving it our all -- I don't think me speaking on other teams or other generations can help. I don't want to put more pressure on us as a team.
"I'm a big believer of controlling what we can, that is the game on Sunday, how we approach it, we started that this week. Giving it everything in every game we've played it. We sometimes haven't got the result we wanted. We looked back at that game and thought how well organised they were [and] took that into the next game."
Stones also said his centre-back partner Harry Maguire deserves respect for ignoring "outside noise" to play a key role for England at the World Cup.
Maguire relied on a degree of loyalty from Southgate to make the final 26-man squad for Qatar after starting just nine matches for Manchester United across all competitions this season.
The 29-year-old was also booed by some England fans when representing his country back in March but has shrugged off the criticism to produce three solid displays here in Qatar against Iran, the United States and Wales.
"I think right from the first game [in Qatar], it was the best response in what he's been doing," Stones said of Maguire.
"All three games he's played in, he's been terrific and it is about us finding that partnership again, whoever we play with. I think we have done in these three games and now it is time for us to keep building and keep improving and that is great credit to him.
"I spoke at length on Harry before, there were a lot of questions that I got asked and playing with someone for so many games at England and been through so many moments with him, knowing what he's been going through for his club and the person he is, it speaks volumes about him.
"To come through that and still believe in himself like I believe in him, like all his teams believe in him, his teammmates at United, and I think there's been a lot of noise from the outside which he's not listened to. He's tried to improve himself and better himself and he's come into this tournament and hit the ground running and that's great credit to him."