The Hoops bowed out of the competition on Wednesday after a 2-0 defeat by Juventus in Turin - losing the tie 5-0 on aggregate.
Despite the result, Neil Lennon's men had the bulk of the play and the chances over the two legs, but Strachan believes the Italian champions were ruthless because of the quality of their squad.
And Strachan, who twice guided Celtic to the same stage of the Champions League, insists the club have been a credit to Scottish football on the biggest stage.
"It was a very strange 5-0 because that is not a reflection of what happened," Strachan said.
"What I saw was a manager being brave and actually spooking Juventus for a good hour at least at Celtic Park and making Juventus play the way they did not want to play.
"If you look at the attempts at goal and possession over the two games, I don't know the stats, but I think Celtic would probably come out on top.
"As Neil said, with the budget he's got, you might miss a couple of chances, you might make a couple of mistakes, whereas with the budget the other team's got, their mistakes are less.
"We can all take a lesson in bravery from what we've seen. It was an unfortunate result over the two legs but they were performances that Celtic and Scottish football can be very proud of."