The former Celtic manager lavished praise on his team but singled out substitute Chris Martin, who netted the winner after being booed by his own supporters, and debutant Stuart Armstrong for plaudits after the game.
"I am very proud, I am delighted for all the players," he told Sky Sports News. "I thought they were magnificent, considering the pressure they were under. They should be really proud of themselves.
"Chris Martin gets a good reception from the players and the staff. That is why we pick him. He is in great company. Kenny Dalglish was booed, so was Gary McAllister, so was Alan Hansen. He must be some player.
"We have got ourselves back in contention and we look forward to the next game now. We can take a lot of things from tonight. These players played extremely well and I think Stuart Armstrong's could be the best Scottish debut I have ever seen."
The win for Scotland moved them back in contention to qualify for the finals, with the Tartan Army now two points behind second-placed Slovakia.