England's Football Association said it was "appalled" and "disgusted" after racist trolls targeted Marcus Rashford, Jadon Sancho and Bukayo Saka following Sunday's Euro 2020 final defeat to Italy.
All three players missed from the spot as Italy clinched the penalty shoot-out 3-2 after the tense final finished at 1-1 after extra time.
"We're disgusted that some of our squad –- who have given everything for the shirt this summer –- have been subjected to discriminatory abuse online after tonight's game," the England FA tweeted.
"We stand with our players."
A separate statement said: "The FA strongly condemns all forms of discrimination and is appalled by the online racism that has been aimed at some of our England players on social media.
"We could not be clearer that anyone behind such disgusting behaviour is not welcome in following the team."
London's Metropolitan Police said it was investigating the "offensive and racist" posts.
"We are aware of a number of offensive and racist social media comments being directed towards footballers following the #Euro2020 final," it said in a tweet.
"This abuse is totally unacceptable, it will not be tolerated and it will be investigated."
England's players have made a strong stand against racism at the tournament, taking a knee before their games including Sunday's final.