The Scots claimed their first victory at Twickenham since 1983 after dominating the Auld Enemy on the 150th anniversary of the first meeting between the rivals, wing Duhan Van Der Merwe crossing for the only try.
Gregor Townsend's underdogs celebrated the win wildly at the final whistle and the only disappointment was that that the scoreline failed to reflect their mastery of opponents who failed to fire a shot.
"You never atone for a game like this. This stays with you for a long time," head coach Jones said.
"But the most important thing is that we get together and we find a way to improve our performance and play like England do when we come up against Italy next week."
Jones returned to a well-worn theme of blaming himself for one of the worst performances of his reign as England were woefully off the pace, shooting themselves in the foot with a high penalty count.
"We just couldn't find a way to get into the game. On a day like this the set-piece will always be important, the contest in the air will be important, the gainline will be important, and we couldn't win any of those areas," Jones said.
"We just seemed to be off the pace and I have to blame myself, I didn't prepare the team well enough.
"The players play the game but sometimes you have those days and we had one today. Scotland played very well.
"They had a particular game plan which they stuck to and executed really well. They had enormous possession in the first half and a big penalty count and we've only got ourselves to blame for the discipline issues. It was just one of those days."
Apart from Billy Vunipola, England's Saracens contingent had not played since the final of the Autumn Nations Cup on 6 December and unsurprisingly they made little impact.
"We're just grateful for the opportunity to be able to play rugby," Jones said.
"Maybe it wasn't the ideal preparation but it is what it is and we've got to be good enough to be able to cope with that. Everyone is a good selector after the game."
Scotland's forwards submitted the home pack but behind the scrum is where the fireworks were lit as Finn Russell, Stuart Hogg, Cameron Redpath and Van Der Merwe swaggered around Twickenham.
"We'd talked a lot in the last couple of weeks about lifting a nation, and I believe we've done that," full-back Hogg said.
"This win is a huge deal to us all. During the week we said that if we got everything right on both sides of the ball we'd give ourselves a chance, and we did exactly that.
"I'm incredibly proud of the boys. We believed we could dome down here and win, but we kept that to ourselves. It was incredible for us."
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