An instinctive flick from Xavi in the third minute settled last night's tie and gave Barcelona a 4-2 aggregate victory, but Strachan was pleased with how his team fared during the second half.
"In the second half I thought we did very well, braver on the ball and we got closer to people. The longer the game went on I thought we got better and better performances.
On leaving out top scorer Scott McDonald, Strachan was adamant he made the right choice.
"It wasn't a night for two strikers. What we wanted to do was to get to a certain point, then bring on our two strikers and play with them, but we never really got to that point.
"I think it was the best way to play," added Strachan.
"I do believe we can get to the last 8, if we allow this team to develop and we add to the squad. I really feel it can be done.
"They now know the secret of playing against good sides: trust yourself and let yourself go. Sometimes you have to play from the heart."