Strachan told his defenders to up their game if they have any intention of retaining their Scottish Premier League championship.
He said: "If you don't defend well, then you have to expect to lose. The way we defended in open play was more than adequate but you can't win any game if you let in four goals from free-kicks.
"We will have to go and analyse our defending at free-kicks because there has got to be a common denominator if you concede four times from set-pieces.
"It was a bit windy today and we will have to look at whether we are doing the right thing in those types of conditions. In some conditions the way we have set up may have worked but it has not worked, that's for sure.
"I know you still have to deliver the ball well and get a head on it but we are hoping that teams have to work harder to score against us.
"In free play Mark Brown has not had a save to make, which is astonishing. It was a strange and exciting game and I'm sure everybody enjoyed it, apart from the Celtic supporters.
"But we can console ourselves with the fact that it was one of our better performances over the last couple of weeks."
The Celtic boss admitted he was baffled when referee Dougie McDonald awarded Aberdeen's third goal - a Zander Diamond header from a Charlie Mulgrew delivery - because he believed the official had already blown for a foul.
Strachan added: "Automatically everybody thought it was a free-kick. That was the indication through his body language.
"Jimmy [Calderwood, Aberdeen's manager] also thought that. Everybody heard that the whistle was blown early before the ball went into the back of the net. I don't know whether it was confirmed on TV.
"We expected a free-kick but it hasn't been given so we just have to get on with it."
Delighted Aberdeen boss Calderwood paid tribute to Mulgrew's deadly deliveries from set-pieces after his side's shock win.
Diamond earned most of the plaudits for his winning brace but it was Mulgrew's crosses for both goals that most impressed Calderwood.
He said: "Charlie has an unbelievable left foot. It was two wonderful free-kicks from him.
"Charlie puts the balls into the box with so much pace it makes it very difficult to defend. It is a massive weapon for us, especially as we have guys like Diamond, Miller, Severin and McDonald who are all good in the air."
However, Calderwood played down comparisons between Mulgrew and Celtic's free-kick expert Shunsuke Nakamura.
He added: "Nakamura has been taking free-kicks for years and Charlie has only been here a few months. He has got a couple of years to catch up on Nakamura yet.
"He works on his free-kicks and we know that when he is on form he will put the ball in the right area for our players to go and attack it."