"Scottish Rugby is appalled by the verbal abuse suffered by Eddie Jones," a statement said.
"The disgusting behaviour of those involved does not represent the values of our sport or its fans. The dignity Eddie and the England team showed on Saturday is in stark contrast to this ugly incident."
Jones, who had led England to 24 victories in 25 games before the 25-13 loss in Edinburgh, was surrounded, apparently by Scotland supporters, at Manchester's Oxford Road Station.
After posing for selfies he was verbally abused before gettting into a waiting car.
Jones attended Manchester United's Premier League game against Chelsea at Old Trafford on Sunday before travelling back to London.
"I'll make sure I won't in future. It's as simple as that," Jones told the BBC. "I'm a human being. I don't consider myself any different from anyone else, so for me to travel on public transport I thought was okay."
(Reporting by Martyn Herman; Editing by Angus MacSwan)
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