Goals from Scott McDonald and Jan Vennegoor of Hesselink had looked to have put the result beyond doubt with a third of the match remaining, only for Kevin McDonald to reduce the deficit courtesy of a predatory finish.

However, in a grandstand finish Celtic held on for the win, leaving a bullish Strachan to jokingly suggest his team, who have won convincingly at Falkirk, Aberdeen at St Mirren - as well as being involved in a thrilling 3-2 defeat to Hibernian on Sunday - need to discover how to play more defensively.

He said: "We have been involved in terrific games both tonight and on Sunday, so we really need to learn how to bore the pants off people and win 1-0, because this exciting football is not good to anybody.

"We really need to shut up shop and scare everyone away from football, but this is just the way we play.

"The idea is to score more than the other team and away from home this year we have done that four times, which isn't bad.

"We have been involved in a lot of good games and we are good box office."

Celtic could have scored a second goal nine minutes before Venegoor of Hesselink eventually struck, but Derek Riordan saw his penalty well saved by Craig Samson after he had been fouled by substitute Danny Griffin.

Samson's opposite number, Artur Boruc, was also in fine form and on the two occasions the ball did get past his grasp, the woodwork saved Celtic.

Gavin Swankie curled a wonderful free-kick off Boruc's far post in the 19th minute and only 60 seconds later, Jan Zemlik's flicked header clipped the crossbar.

Boruc looked far more composed than he was at Easter Road on Sunday, when his mistakes gifted Hibs two goals and Strachan was delighted with the goalkeeper's contribution.

He said: "Artur is a top-class goalkeeper and he has absolutely fantastic mental strength."

Strachan now hopes injured trio Jean-Noel Perrier Doumbe, Paul Hartley and Aiden McGeady will be fit enough to face Dundee United on Saturday having missed this game.

Dundee manager Alex Rae wants his young players to learn from this defeat, as he believes the two mistakes which led to Celtic's goals were the only blemishes on a fine performance.

McDonald was left unmarked to head in Riordan's free-kick, while Rae was left to rue his side being caught with the ball, as McDonald crossed for Vennegoor of Hesselink to score with an easy finish.

But the Dundee boss was delighted with the fighting qualities of his side and wants them to take that attitude into their future games.

He said: "The players were outstanding and at 2-0 I thought we were down, but they kept going forward and managed to get back in the game.

"Two mistakes have cost us though, as it was a free header in their box for the first goal and we gave away possession for the second.

"Unfortunately when you are playing at this level you get punished for that, but it is a good learning curve for us and I think our young players came of age tonight."