Penalty takers Bukayo Saka, Jadon Sancho and Marcus Rashford were all subjected to racist insults on social media, after the Three Lions suffered a penalty loss in Sunday's final against Italy.
Smalling, speaking with the BBC, said he was "surprised and not surprised at the same time" at the abuse his compatriots had suffered.
He called upon authorities to make sure all individuals are held accountable for what they post online.
"I hope this opens up the conversation around acceptance," he added, echoing sentiments expressed by Formula One world champion Lewis Hamilton.
"We need to work towards a society where no matter your ethnicity or heritage, you don't have to prove your value or place in society only by winning a game."
Smalling suggested professional athletes are being left impatient by the lack of progress being made to combat the issue of online abuse.
"Even though there has been a lot more movement and standard action being taken by a majority of players around the world, I feel like we are still asking the same questions and there is not enough action being done," he said.
"Even down to simple things. We are verified on Instagram. We are held accountable for all our views and opinions.
"Someone anywhere in the world can say something and it will immediately come to my phone, which is next to me. They are not held accountable."
Smalling pointed out that all England's players should be praised for what they have achieved this summer - reaching a first major final for the nation for 55 years.
"Win, lose or draw, whether we won the Euros or not, all of the players should be held up in such high regard," he said.
"And they are by the majority because of how they have united the country.
"But it is so disappointing that a few can overshadow what has been a positive summer.
"The racism only reminds us of the change that still needs to happen and how we all still need to do our bit and educate ourselves."
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