The Hoops needed substitute Jiri Jarosik to rescue a point on a fraught afternoon against managerless Hibernian at Parkhead.
Strachan's men were shocked in the 20th minute when Hibs defender David Murphy, ironically a Parkhead target, crashed a shot from the edge of the box past Mark Brown and in off the crossbar.
Celtic have now dropped nine points from their last 15 and Strachan is in little doubt where the problem lies.
He said: "It was a great start to the game for the first 20 minutes then they go up the park and score. It was a good finish by the lad but we were a bit shocked, thinking how did that happen?
"In terms of character both teams were equal but in terms of chances we were out of sight. We won that by a long way but we couldn't finish off the moves.
"Our problem right now is letting in goals. I'm concerned about that.
"If we sort that out then I'm sure we will score goals. If you want to be top of the league you have to defend better than we are doing. If you are playing against us you will say 'there is a chance of scoring against them'.
"It puts a lot of pressure on our lads up front to know that you must score two or three goals to win the game. And when you are not scoring, it puts a lot of pressure on the defenders not to let a goal in.
"I need to find out a formation from what we've got or do something else."
Hibs assistant boss Tommy Craig, in temporary charge following the surprise resignation of John Collins this week, was rather coy when asked if he would be interested in the Easter Road hotseat full time.
Craig said: "The chairman spoke to me and asked me to take the team over the festive period. Full stop.
"If the job ever came up it would be discourteous of me not to speak to anyone.
"My CV is in, it's 14 months long. They know me and they know what I can do."