BBC Sport believes that Caldwell and two Celtic officials were told in the dressing-room that they had been reported for violent conduct.
However, Strachan maintains that Celtic did not hear anything from the SFA until Friday morning.
"At no time on Wednesday night were they told they had a red card, they were not shown a red card.
"The first I saw it was on the text on Thursday, someone spoke to the media from the SFA - Drew Herbertson," he said.
"As for Gary Caldwell, it first came to his at tention on Sky Sports News.
"At 11 o'clock on Friday morning the club had not been contacted. We find that extraordinary. It would have been nice to send us an email telling us first.
"When you make a decision, the first port of call would be the players and the club.
"I want to know who decided between the game at night and 11 o'clock in the morning, who watched the tape and who decided it would be a one-match ban. We'll not complain but I think there needs to be clarity."