England have come under intense pressure for their underwhelming performance against Scotland, with expectations high about the team's prospects having reached the 2018 World Cup semi-finals.
Sterling said the doom and gloom needed to subside, pointing to previous champions at both European Championships and World Cups who had started slowly.
England have four points from their opening two games in Group D, with Sterling scoring the winner in their opening 1-0 victory over Croatia, ahead of Tuesday's group finale against the Czech Republic.
"[England manager] Gareth [Southgate] showed us some stats on teams that have gone on to do well in the tournament and where they were after the first two games," Sterling said.
"It just shows that it's still early days and we've got a lot to build on and I truly do believe we can do that."
He added: "This was another scenario where we've got four points, it's not the end of the world. He tried to make us look at all the positives.
"He's just showing us in previous tournaments that it's not every team that wins their first few games that goes on to win.
"Sometimes, teams that have drawn their first two games have gone on to win so we've just got to stay motivated, be happy and enjoy our football."
Portugal drew all three of their group games at Euro 2016, before storming home and beating hosts France in the final.
Denmark's 1992 European triumph as well as the Netherlands in 1988 were other examples of eventual champions starting slow.
"I do feel there's a bit of an overreaction … there's more of a panic on the outside than inside the building," Sterling said.
"I don't see anyone in the camp that feels any pressure or feels hard done by. The best thing we can do is focus on the training field.
"The more you listen to outside noise, the more it can affect you. The positive is that we can go out on Tuesday, get a good win and that second game is all forgotten about."
City this week made their case in an appeal against a two-year ban from UEFA competition, after being found to have breached Financial Fair Play (FFP) rules.
The outcome of that challenge at the Court of Arbitration for Sport is reportedly not expected until July, by which time City's reign as Premier League champions is likely to have been ended by Liverpool.
If City are forced to miss two Champions League campaigns, such a blow could tempt their top players to look elsewhere. Madrid have been frequently linked with forward Sterling, while De Bruyne has hinted he would consider his future if the two-season ban was upheld.
Former City and England manager Eriksson says Sterling and playmaker De Bruyne can choose their own destiny, but cautioned that they are already playing at the highest level in domestic club football.
“Well, they will play for Real Madrid if they want to do it, but I would be disappointed," Eriksson told Stats Perform News.
"I don't know - I really hope they stay in England. When you look at it so far, and for many years now, the Premier League is the best league in the world, no doubts about that - most popular, the best league to see.
"Other leagues are good, but how many people are looking at Spanish football if it's not Barcelona or Real Madrid, maybe Atletico Madrid? I don't think many.
"Bundesliga, it's a little bit the same if [Borussia] Dortmund's not playing, if Bayern [Munich] is not playing, are you sitting looking at it? In England it's different because any team can beat any other team. It's good football and it's always a fight, a good fight in England."
To lose Sterling, De Bruyne, or both, would be a huge setback for City on the pitch, but Eriksson knows Pep Guardiola is just as important to the four-time Premier League winners.
Manager Guardiola has a year left on his City contract and has not ruled out signing an extension.
The former Barcelona and Bayern Munich boss appears likely to at least see out his current deal, having this week brought in his mentor Juanma Lillo as a new assistant coach, but much could still happen to change that.
"Of course it's important," Eriksson said of the Spaniard's future. "He's considered one of the best, if not the best coach in the world. He has been so for a long time.
"To lose him before the contract finishes would be bad for Manchester City: bad for the fans, bad for the players, bad for the club. Not sending out a good message.
"I hope they will do everything to try to keep him at least until the contract finishes."
It gave England's women a breakthrough moment and led to acclaim from across football and far beyond, with Harry Kane, Boris Johnson and David Baddiel among those joining in the celebrations.
Baddiel famously joined fellow comic Frank Skinner and indie band the Lightning Seeds in creating the 1996 Three Lions hit song, with the 'It's coming home...' lyric weighing heavily for over a quarter of a century.
In a letter to the England team, The Queen said they would serve as inspirational figures for generations to come.
She wrote: "My warmest congratulations, and those of my family, go to you all on winning the European Women's Football Championships.
"It is a significant achievement for the entire team, including your support staff. The championships and your performance in them have rightly won praise.
"However, your success goes far beyond the trophy you have so deservedly earned. You have all set an example that will be an inspiration for girls and women today, and for future generations.
"It is my hope that you will be as proud of the impact you have had on your sport as you are of the result today."
England men's captain Harry Kane, whose side were beaten on penalties by Italy at Wembley in last year's European Championship final, said the scenes this time around were "absolutely unreal".
The striker spared high praise for Ella Toone, whose precise lob gave England a 1-0 lead in the 62nd minute, saying the Manchester United forward should "take a bow for that finish".
His England colleague Raheem Sterling hailed the group as "history-makers". Kane and Sterling will be among the England team targeting World Cup glory later this year.
Former England defender Gary Neville called it "a seismic moment for sport in this country" while outgoing Prime Minister Johnson said it was a "stunning victory".
Gary Lineker, who reached the World Cup semi-finals with England in 1990 and won the Golden Boot at the 1986 tournament, harked back to a famous comment he once made about German success.
Appropriating it for the Lionesses, he wrote: "Football is a simple game. 22 women chase a ball for 90 minutes and, at the end, England actually win."
The Three Lions anthem might have to be retired now that England have triumphed on such a major stage.
Baddiel, Skinner and the Lightning Seeds have had good mileage out of that summer smash hit, from back when England hosted the men's Euro 96 tournament.
Baddiel wrote on Sunday evening: "It's come home. A sentence I thought I'd never write. I've gone. Thank you Lionesses."
