The decision was announced on Wednesday, with reports appearing early in the day before an official announcement from Whitehall ahead of a similar announcement made by the Scottish Government in the afternoon.
Under the new guidelines, travellers from the US or EU who are fully vaccinated will be able to skip self-isolation after they arrive in the UK.
Speaking at the official opening of a new eye centre at the Golden Jubilee Hospital in Clydebank, Humza Yousaf told the PA news agency: “We’d rather the UK Government had worked with us and we could have got to a joint position and communicated that jointly, that would have been a better position to be in.”
He added: “In terms of communication, I would have preferred it to be done a way where the four nations did that jointly.”
The decision, the Health Secretary said, addresses an “anomaly” over vaccines.
“I think there was a bit of an anomaly there for people who had been vaccinated from vaccines that we would recognise here in Scotland,” he said.
“I’m pleased that anomaly has been fixed.”
Travel has been regarded as one of the main drivers of cases and new variants throughout the pandemic, with people often bringing the virus – and its different mutations – into other countries.
But the Health Secretary said: “There is a difference when it comes to amber list countries and red list countries, so when there is countries that we’re particularly concerned about because of case numbers or maybe a new variant, of course that exemption will apply there.”
When asked if he was confident the traffic light travel system would be able to counter any of the risks of the new rules, Mr Yousaf said: “I can’t stand here truthfully and give you a cast iron guarantee that a new variant from somewhere across the world would never make its way to the shores of somewhere in the UK.
“That’s not something I can give you a cast iron guarantee on, anyone who did say that would be being untruthful.”