Scott McDonald struck his second hat-trick of the season, but Strachan bristled at the suggestion that his decision to rest McDonald in Lisbon had been vindicated before praising Killen for his part in the victory.
He said: "I don't have to justify myself to anybody, just the players.
"I said the priority was the SPL. I would have loved to have played Scott the other night but he has had a lot of hard games.
"But I don't have to justify myself.
"He wouldn't have scored it if he hadn't had Chris Killen playing alongside him.
"I thought he was excellent. Last season, if Jan Vennegoor of Hesselink was injured we couldn't have played the way we did today, but Chris Killen allows us to do that.
"So I would say he was the most important person in the team for us today."