The Scottish champions fell behind to Erik Nevland's goal within two minutes and Bobby Zamora struck a fine second in the 32nd minute.

Barry Robson's free-kick reduced the arrears before the break but Leon Andreasen sealed a home win with five minutes left.

The game came less than 24 hours after Celtic's 2-0 victory at Southampton, and Strachan made only one change to his starting line-up.

Strachan told Sky Sports News: "Both sides were a bit rusty with their passing, us especially in the first 20 minutes.

"I think we had lazy minds from last night. We finished the game at 10 o'clock and we were up again this morning, at nine o'clock we were on the go again.

"So we had lazy minds for the first 20 minutes but once we cleared that, I thought we put a good show on."

But Strachan did not regret setting the tough physical challenge for his players as he bids to get them into shape for their title defence.

"It's like training. I asked them to train very hard on Monday and then very hard on Tuesday.

"We don't take days off, and remember they only played 45, some of them played 60.

"Maybe the nervousness - training is different - because there is a nervousness to playing football, so there is a mental stress that goes along with it.

"Maybe we didn't give them a chance to relax after the game."

Celtic are thought to be continuing their attempts to sign Auxerre defender Gabriel Tamas, with talks with the Romanian international proving protracted.

But Strachan refused to comment on the transfer situation.

"I have said all along we will try to bring players in, but we will not name them because it puts pressure on everybody.

"We will show respect to other clubs that we don't name players until the deal is done or the club itself says 'you can go and speak to them'."