Marcus Rashford, Jadon Sancho and Bukayo Saka were all subjected to abusive posts in the wake of their missed penalties in the shoot-out against Italy on Sunday night.
The Home Secretary tweeted on Monday to say she was "disgusted" that players who had "given so much for our country this summer have been subject to vile racist abuse on social media".
However, her tweet has prompted an angry response from Aston Villa and England defender Mings, who accused Mrs Patel of 'stoking the fire' after she refused to condemn fans who booed the England team taking the knee ahead of kick-off.
"You don't get to stoke the fire at the beginning of the tournament by labelling our anti-racism message as 'Gesture Politics' and then pretend to be disgusted when the very thing we're campaigning against, happens."
Speaking in June, Mrs Patel said: “I just don’t support people participating in that type of gesture, gesture politics, to a certain extent, as well.”
Asked whether England fans were right to boo the national team, she added: “That’s a choice for them, quite frankly.”
The symbol of anti-racism solidarity gained attention in American football in 2016 as players protested against police brutality and racism in the US.
The act has since spread further and was adopted by footballers in the UK, partly to demonstrate that racism should not be tolerated in the sport.
Figures within football, from the Government and even the Duke of Cambridge have condemned the abuse aimed at the England players since Sunday's loss to Italy.
Mings also said: "I’m still struggling to find the words to express my emotions from the past month. I’m so proud of everyone who has contributed to the joy and togetherness this team has bought to millions. We have celebrated, smiled, cried and cheered together & for that, I’m so so proud.
"But waking up today and seeing my brothers being racially abused for being brave enough to put themselves in a position to help this country, is something that sickens, but doesn’t surprise me. We have literally made history. We’ve gone where no one else has gone. Take that in."
Prime Minister Boris Johnson also condemned the abuse during his Downing Street press conference.
"To those who have been directing racist abuse at some of the players, I say shame on you and I hope you will crawl back under the rock from which you emerged," he said.
However, fotballer-turned-pundit Gary Neville criticised Johnson's leadership, telling Sky News: "Gareth Southgate and the players a few weeks ago, about five days on the trot, told us they were taking the knee to promote equality and it was against racism.
"The Prime Minister said it was OK for the population of this country to boo those players who were trying to promote equality and defend against racism. It starts at the very top.
"I wasn't surprised in the slightest that I woke up to those headlines; I expected it the minute that the three players missed."
Twitter said it had proactively removed more than 1,000 posts over the past 24 hours which violated its policy and also taken swift action to permanently suspend a number of accounts.
Facebook, which owns Instagram, said it tries to remove harmful content as quickly as possible and encouraged people to use the tools it offers to block abuse.
The Metropolitan Police is investigating the abuse, while Wolves said one of their supporters had been reported to West Midlands Police after posting a racist tweet and Leyton Orient have already issued a lifetime ban to a fan.