Freedom Day July 19, the same day pandemic restrictions are due to end, had been put forward as a potential bank holiday if England had beaten Italy on Sunday night.
On Monday, Downing Street said a national day off was not being considered to commemorate the team’s remarkable competition run.
The Prime Minister’s official spokesman said: “We’ll be talking to the FA to identify a suitable way for the Prime Minister to thank the players and coaching staff for their efforts.
“But a bank holiday is not something that is being considered.”
Some England fans targeted players with horrific online abuse after the team lost to the Italians on penalties.
Racist comments were made to Bukayo Saka, Marcus Rashford and Jadon Sancho after they missed their spot kicks.
The Metropolitan Police said it is investigating the abuse and added "it will not be tolerated".
Boris Johnson said: "This England team deserve to be lauded as heroes, not racially abused on social media.
"Those responsible for this appalling abuse should be ashamed of themselves."