The Parkhead side were 2-0 down after just eight minutes in a disastrous start to the match - Brandao's drive from the edge of the box in the fifth minute followed three minutes later by a Cristiano Lucarelli header.

The Hoops are still looking for their first away win in the group stages of the tournament after 13 attempts and will now be concentrating on the visit of AC Milan in their next Group D match.

Although Celtic lost to Manchester United in their first group game last season and still qualified for the last 16, on this evidence the Scottish champions will have a more difficult task emulating that feat this time round.

In a one-sided first half Celtic could not have complained if they had been five down at the interval.

Shakhtar had beaten Celtic 3-0 at the same stage of the tournament three seasons ago and they made in-roads in to beating that score right from the kick-off.

Celtic skipper Stephen McManus took an uncharacteristic and needless risk at the edge of his own penalty area, giving Fernandinho the chance to put Brandao through on goal and his fellow Brazilian quickly dispatched the ball past Artur Boruc.

Three minutes later, with Celtic in disarray, defender Razvan Rat's deep cross from the left found the head of Lucarelli who guided the ball past the flailing Boruc from 12 yards out.

Another Rat cross from the left found Lucarelli, but this time Boruc saved the Italian's weak effort before Brandao had the ball in the net again, only to be ruled offside, although television pictures suggested the decision was wrong.

Shakhtar's big-money stars were turning on the style and there appeared to be no respite on the horizon for the bedraggled Hoops.

As Donetsk pressed again, Srna drove a powerful volley from wide on the right across the Celtic six-yard box, the ball ricocheting a couple of times before landing in the arms of Boruc.

Celtic's first effort on goal came in the 28th minute, McDonald's drive from the edge of the box being deflected for a corner.

Donetsk defended the set-piece easily enough but moments later Vennegoor of Hesselink should have scored from Shunsuke Nakamura's driven free-kick, the Dutchman heading high over from close range when a goal looked more likely.

There was a short lull in proceedings but in the 39th minute Boruc produced a magnificent diving save from Rodrigues Jadson's volley after yet another fine cross from Srna had found Celtic in tatters.

The visitors welcomed the half-time whistle like a punch-drunk boxer and after the restart they went looking to reduce the deficit.

However, Shakhtar soon had them on the back foot again but without the immediate results of the opening half, Srna hitting the side net with an angled-drive with his first poor piece of play in the game.

In the 53rd minute Brandao missed a sitter after Mariusz Lewandoswki had sent in a cross straight on to the Brazilian's head.

Celtic midfielder Scott Brown, booked in the first-half for a lunge at Srna, was lucky on two occasions not to pick up a second yellow - Spanish referee Alberto Undiano taking a lenient stance on the Scotland international's indiscretions.

Much of the danger, as in the first-half, was coming from Srna down the right with Celtic defender Lee Naylor struggling badly to cope with the Croat.

The Hoops defence were defending more doggedly now and they had to as the Donetsk fans demanded a third goal.

McGeady replaced Nakamura in the 64th minute as Donetsk swapped Jadson for Nery Castillo but the flow of the game - towards Boruc - remained uninterrupted.

As the tempo of the game dipped a little to Celtic's advantage, Vennegoor came close with a header, Naylor's first dangerous cross of the game finding the Dutchman free inside the penalty area.

In the 80th minute Castillo drilled in a 25-yard drive which Boruc did brilliantly to parry, Naylor helping his defence with his saving tackle on the lurking Brandao to stop the Brazilian tapping in number three.

Castillo then worked some space at the edge of the Celtic box twice in a couple of minutes, but again fired over on both occasions.

By then the points were safe and Celtic turned their attention to the visit of the Italians as their next hope of getting off the mark.