Manchester United was forced to settle for a point in Ukraine after it squandered the advantage to finish 1-1 at Shakhtar Donetsk.
Danny Welbeck gave United a first half lead but the home side equalized through Taison with 14 minutes remaining.
Ryan Giggs made his 145th Champions League appearance to set a new competition record but he failed to find a way to inspire United to victory.
"The team stood up well tonight," United boss David Moyes told Sky Sports.
"We got a good goal early doors. It looked like we would have stopped them from scoring until the goal.
"We said at half time we had to keep the ball better. I'm disappointed we didn't pass it better. If we got the second goal from Robin [Van Persie] we would have seen it out."
United has suffered its worst start to a Premier League season in 24 years and was beaten at home by West Bromwich Albion last weekend.
But goalscorer Welbeck was encouraged by his side's latest display.
"In the end it was a decent result," he said.
"We got the goal early. They then got a goal and that's the disappointing part. I don't think many teams come here and get three points -- we would have liked to have got three points."
Elsewhere, Bayer Leverkusen secured a 2-1 home win over Real Sociedad thanks to a last minute strike from Jens Hegeler.
Simon Rolfes had given the German side the lead on the stroke of halftime before Carlos Vela equalized for Sociedad.
Cristiano Ronaldo scored twice as Real Madrid eased to a 4-0 win over FC Copenhagen to make it two wins out of two.
Angel Di Maria also netted twice as Real moved four points clear at the top of Group B.
That's because Juventus was held to a 2-2 draw by Galatasaray in Turin.
The home side had looked set for victory after goals from Arturo Vidal and Fabio Quagliarella had canceled out Didier Drogba's opener.
But Roberto Mancini's side claimed a dramatic equalizer late on when Umut Bulhut fired home.
Zlatan Ibrahimovic scored twice and Marquinhos grabbed the other as Paris Saint-Germain thrashed Benfica 3-0.
The French side have won both of its opening two group games and sits three points clear of Olympiakos in second, which won 3-0 at Anderlecht.
The night belonged to Olympiakos star Kostas Mitroglou who became the first Greek to score a hat-trick in the Champions League.