(CNN) -- Arjen Robben said it all -- "We didn't expect an easy game like that."
Robben could have been forgiven for expecting more of a challenge from one of the most expensively assembled teams in European football.
But the Dutchman will not lose too much sleep over the way Manchester City capitulated against a Bayern Munich which simply oozed class.
Bayern, which won the European Champions League last year, claimed a 3-1 win -- a result which flattered City for the most part.
"The first 70 minutes we played some terrific football," Robben told Sky Sports.
"We were so dominant against a big team in Europe. We didn't expect an easy game like that.
"It is a compliment to our team but we expected more from City. We didn't give them any space, we pressed them right up to the goalkeeper and they just kicked it away. Sometimes they gave us too much space and we used space well."
City's disastrous flirtation with the Champions League was supposed to end with the arrival of new manager Manuel Pellegrini.
It has failed to make it past the group stage in its two previous attempts and it faces a challenge once more.
Make no mistake about it -- if this was a boxing contest then the referee would have brought this bout to a halt at halftime.
Bayern, which is highly fancied to successfully defend its title this year, produced a level of performance which City could only dream of.
From the moment Franck Ribery's drive somehow flew through the grasp of City's goalkeeper Joe Hart, Bayern was rampant.
City, which was beaten by Aston Villa in the Premier League at the weekend, looked off the pace and unable to keep up with their opponent.
That Bayern managed to score just once in the opening 45 minutes was the only surprise -- but it soon made sure of victory with the help of some inept City defending.
Gael Clichy was the guilty party on this occasion, failing to track the run of Thomas Muller, who was afforded the freedom of the penalty area before firing past the stranded Hart.
City was stunned and Robben added a third just four minutes later after unleashing a rasping effort which beat Hart at the near post.
To its credit, Pellegrini's team did offer a response with substitute Alvaro Negredo curling home a delightful effort with 11 minutes of the contest remaining.
City sensed an unlikely comeback with four minutes to go when Jerome Boateng was shown a straight red card after taking out former teammate Yaya Toure.
David Silva curled the free kick against the crossbar but Bayern negotiated the final few minutes to record an emphatic victory.
"We knew they were a really good team and they showed that. That is why they are champions," City defender Micah Ricahrds told Sky Sports.
"They didn't play with a striker and there was so much movement. It felt like they had an extra man and I wish them all the best.
"Hopefully we can now improve. We tried, there were some tired legs out there but we can do better than that."
In the group's other game, CSKA Moscow overcame Viktoria Plzen 3-2 to move level on points with City.
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.