"The disgusting behaviour of those involved does not represent the values of our sport or its fans," Scottish Rugby said in a statement.
"The dignity Eddie and the England team showed on Saturday is in stark contrast to this ugly incident."
Jones said he wouldn't take public transport again.
"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 OK. But I'll make sure I won't in future. It's as simple as that," Jones said on Wednesday.
"I can't because it was shown on Sunday what happens when I do. That's the world we live in. I was massively surprised. It wasn't comfortable."
When asked whether the abuse was physical or verbal, Jones replied: "A bit of both.
"It's part of the challenge. As an Australian coaching England, there were always going to be challenges and that's just one of them."
Jones casts his experience after an interview last week by Scotland and British and Irish Lions great Gavin Hastings, while also referencing prop Simon Berghan's pre-Six Nations match claim that "everyone hates England".
"As a supporter of one of his opponents, you just want to rub his face in the dirt," said Hastings, who won 67 caps in a distinguished career spanning nine years.
Jones believes Hastings and Berghan should have chosen their words more carefully due to the influence they wield.
"It magnifies that if you're in a position of responsibility, you've got to be careful what you say," he said.
"Because if you talk about hate and you talk about rubbing peoples' nose in the dirt, and all those sorts of things, it incites certain behaviours and are they the sorts of behaviours that we want to see?"
Part of Jones' frustration with Sunday's events is due to his willingness to engage with supporters.
"I never knock back a request for a selfie unless I'm racing to somewhere. So I try and do the right thing by the fans but, if this happens, then you've got to have a look at your own safety," he said.