The back-to-back Six Nations champions suffered a first Calcutta Cup defeat in a decade after failing to recover from a poor first-half showing.
Scotland were 22-6 to the good at the midway point and, despite an improved showing for England in the remaining 40 minutes, they were able to see things through for a famous triumph.
Jones, beaten for just the second time in 26 Tests since taking charge after the 2015 Rugby World Cup, confessed at full time that he could have few complaints about the scoreline.
"Congratulations to Scotland," he told ITV Sport. "They were too good for us. Unfortunately we were not in the game in the first 40. Scotland played well. Full marks to Scotland.
"We knew what we were going to get but we didn't meet the challenge today for some reason. Second half I was very proud of the effort of the boys. We really stuck in there and won the second half."