A first-half header from McDonald and Jan Vennegoor of Hesselink's cool finish - not long after Derek Riordan had a penalty saved by Craig Samson - saw Celtic progress to the quarter-final stage of the competition last night.

A spirited Dundee side pulled back a goal through Kevin McDonald, but the robust Celtic back line played out the remainder of the game without conceding - much to their Australian attacker's delight.

He said: "We rode our luck a couple of times, but it is good to see after losing two games in a row that we can show a bit of fight to come through and win."

Celtic were criticised for successive away defeats to Shakhtar Donetsk and Hibernian, in particular for their apparent inability to keep a clean sheet on the road.

Gordon Strachan's side have not shut out an opposition team when playing away from Parkhead since last October.

McDonald is not surprised at the flak directed Celtic's way, because he believes the club's stature dictates that any problems are always going to be magnified.

He said: "Because we are such a high-profile team and have won the league for the last two years, everyone expects us to win every game - and if we don't, it's a crisis."

McDonald was delighted with his own performance at Dens Park, setting up Vennegoor of Hesselink's goal.

"I am trying to work on being able to see the pass rather than having my eyes on goal all the time - and I think at this level it is important to see other people and put them in," he said.

Dundee pushed Celtic all the way to the final whistle and twice struck the woodwork, Gavin Swankie and Jan Zemlik the unfortunate duo denied.

Zemlik's night ended in further disappointment when he was sent off in the final minute after receiving his second caution of the game.

But even that sour note could not dampen the spirits of Dundee manager Alex Rae, who was delighted with his players' efforts.

He said: "The young players such as Kevin McDonald, Scott Robertson and Gary MacKenzie were brilliant - and so were the older ones, who put in a really hard shift."