Nicola Sturgeon led the criticism which means students from other European countries will no longer be able to easily work or study in the UK as part of their education with the same barriers facing British students on the continent.
Boris Johnson said today the UK was losing out financially on the initiative and unveiled a new "Turing" scheme replacement for British student.
But the First Minister said: "Ending UK participation in Erasmus - an initiative that has expanded opportunities and horizons for so many young people - is cultural vandalism by the UK government."
Scottish Greens education spokesman Ross Greer described the decision as "a pointless, spiteful move from British isolationists."
He added: "A formal request from Scotland to continue taking part in whatever way we can should be a priority in January."
Mr Johnson said the Erasmus programme would be replaced by a worldwide scheme named after Bletchley Park code breaker Alan Turing.
Mr Johnson said "it was a tough decision" to pull out of the programme, for financial reasons.
He added: "We are doing a UK scheme for students to go around the world, it will be called the Turing scheme.
"Students will have the opportunity not just to go to European universities, but the best universities in the world."
The Erasmus exchange programme, which was established in 1987, gives students in Europe the opportunity to study or work abroad in another European country. The programme is worth about £243 million a year to the UK.