The 19-year old Dundee United defender came on for the final 23 minutes of the Scots' 1-0 friendly win over Poland in Warsaw on Wednesday night in what was a quantum leap from Scotland's League One just 12 months ago.
Robertson started his senior career with Queen's Park before moving to Tannadice this past summer and he has now been warned to continue working hard to develop in order to keep going from strength to strength.
"It was eight months' hard graft for him to get there," Strachan said.
"I know other people take a bit longer but he's had that hard graft at Queen's Park. I always felt, from the first time I saw him, that he was a bit different.
"All he has to do now is keep going. If he relaxes, then the game bypasses you. It's up to him to keep going.
"We've enjoyed having him in our company this week. He's been good. When he first picked it up [after coming on], I thought 'that's good'. There are no grey areas there.
"We told him the night before at training: 'Don't think about what an international player does. You do what you're good at. Get forward, crossing, take people on, get back'. So he did that when he got on."
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