Speaking on The Sunday Show, however, Mr McKee refused to be pressed to strongly criticise the fans who travelled south.
Thousands of Scotland fans gathered in central London on Friday ahead of the clash between Scotland and England at Wembley as part of the Euros championships.
Mr McKee said: “Well, fans, like everyone else, should follow the rules and regulations absolutely should. That’s the way to beat the virus. There are covid restrictions in place for very good reason and everybody, fans included, should follow these restrictions."
First Minister Nicola Sturgeon has previously criticised other football fans who have gathered in public places and, ahead of Friday’s game, urged Scotland fans without a ticket for the match not to travel south.
However, when asked if he was “disappointed” when he saw the pictures of thousands of fans gathering in central London, Mr McKee said: “It doesn’t help the situation with regards to controlling the virus, absolutely.”
On Friday, Ms Sturgeon said: “The virus doesn’t care about football, it's not going to give you a free pass because you're there to celebrate the football match.”
She added: "It's only natural that many of us want to watch this game with friends - that sense of being in a shared experience is one of the many things that make watching our national team so special. But please remember if you're watching the match today continue to take care.”