Shakhtar 2 Celtic 0: Shakhtar Donetsk struck twice in the first eight minutes to record a comfortable victory over Celtic in their Champions League opener.
Brazilian striker Brandao opened the scoring for the Ukrainians in the sixth minute, beating keeper Artur Boruc with a rising shot from the edge of the box after Celtic's defence gave the ball away.
Cristiano Lucarelli added a second with a diving header two minutes later following a pin-point cross from Razvan Rat.
Celtic, who squeezed into the Champions League by beating Spartak Moscow in a penalty shootout in the third qualifying round, have now lost 13 of their last 14 away matches in Europe's premier club competition.
Elsewhere in the group, AC Milan opened the defence of their crown with a stylish 2-1 win over Benfica thanks to first-half goals by Andrea Pirlo and Filippo Inzaghi.
Pirlo bent a free kick into the top corner on nine minutes and Inzaghi, who scored both in Milan's 2-1 win over Liverpool in last season's final, grabbed his 43rd in this competition on 23 minutes after a run from Kaka and Pirlo's unselfish pass.
Substitute Nuno Gomes slid in to score with the last kick for Benfica but Milan still deserved to win by more.
Benfica had created some good chances before their consolation strike, with tall striker Oscar Cardozo hitting the post with a header and former Milan midfielder Rui Costa testing Dida with a long-range effort.
The seven-times winners were generally comfortable throughout though and could have scored several more with Inzaghi missing three good chances inside the box.