Head coach Eddie Jones says England's first home loss to Scotland since 1983 will haunt his side.
The hosts were beaten 11-6 in their opening game of the Six Nations, with Scotland wing Duhan van der Merwe scoring the only try of the game at Twickenham on Saturday.
"You never atone for a game like this. This stays with you for a long time," Jones said.
The coach added he would "take responsibility" for the defeat.
"I didn't prepare the team well enough," Jones told BBC Radio 5 Live.
"We just had one of those days. We don't have many, but we had a bad day today."
Defending champions England conceded 11 penalties, compared with Scotland's four, in a lacklustre performance.
Jones said the visitors "played tough, edged the set-piece and won in the air".
"We just could not get in the game. We were not at the races today," said the 61-year-old Australian.
"I thought we fought back into the game well. With the possession and territory they had, we hung in the game and had a chance to win at the end, which is a great credit to our players considering we were off the pace."
England host Italy in their next game on 13 February (14:15 GMT) and Jones says his side "will do everything we can" to get their first win of the 2021 tournament.
He added: "If you look at the world at the moment, we are just grateful we can play rugby. We will just suck it up.
"We have Italy next and we will be ready for the next Test match. We will do everything we can."
'Outplayed' - social reaction
Princess Anne, a regular at Murrayfield, was watching from the sofa rather then the best seats.
Brian Moore, part of the England team that famously lost to Scotland at Murrayfield in 1990, was magnanimous in defeat.
Ireland's Simon Zebo, a team-mate of Scotland fly-half Finn Russell at Racing 92, said it with flowers.