The result leaves the Hoops bottom of Group C with just one point from three games ahead of their return match with the Germans next month.

“It is very difficult for us now,” Rodgers said.

“The game in Germany was always earmarked as a game that was going to be tough for us away from home and the home games were going to be important for us.

“It wasn’t to be tonight and we just didn’t cope with them. Our next game is over there which I expect will be very tough again and we will try to do the very best that we can.”

“The best team won – I don’t think there is any argument about that,” Rodgers, whose side face rivals Rangers in the League Cup semi-final on Sunday, said.

“My players will learn a lot from that defeat. No matter how good we play there are still elements we need to be able to compete consistently at this level.

“I said from day one that we are in the process of building something here.

“It was absolutely brilliant to qualify and we gave absolutely everything out there but sometimes teams are better than us and tonight – no disrespect to my players – that was the case.

Here’s a look at what else happened in the Champions League on Wednesday:

GROUP A

Paris Saint-Germain coach Unai Emery acknowledged that his team are not yet up to the standard expected of serious Champions League contenders despite their 3-0 win over Basel.

Goals from Angel Di Maria, Lucas and Edinson Cavani, with a late penalty, gave PSG an ultimately comfortable victory that keeps them on course to qualify for the last 16 from Group A.

Quarter-finalists in each of the last four seasons, the French champions will likely secure their place in the next round if they pick up a point when they face Basel again in Switzerland next month.

“It is an important three points but I am not as happy as I’d like to be,” Emery said after seeing his side struggle in the first half and then improve as the game went on.

“The first half was not good. That’s true. We were saved by the posts but we scored, and at 1-0 the match opened up for us and we had chances.”

The Gunners, who are now unbeaten since the opening game of the season two months ago, top the group with seven points.

Paris Saint-Germain also have seven points.

GROUP B

Vincent Aboubakar scored twice as Besiktas beat Napoli 3-2 to deny the Italian club a chance of advancing from the group stage in record time.

Aboubakar, a Cameroon international on loan from Porto, scored the winner four minutes from time after having also restored Besiktas’ lead late in the first half.

It was the Turkish side’s first win in the competition since 2009.

If Napoli had won, it could have become the first team in Champions League history to advance from its group after just three matches.

Now, Napoli has just a one-point lead over Besiktas, with Benfica two points back after its 2-0 win at Dynamo Kiev.

After Adriano’s opener for Besiktas, Dries Mertens and Manolo Gabbiadini scored temporary equalizers for Napoli.

In Kiev, Eduardo Salvio converted a penalty and Franco Servi also scored in Benfica’s first win of the campaign.

GROUP D

Bayern Munich coach Carlo Ancelotti said their 4-1 romp against PSV Eindhoven in the Champions League was the reaction he was looking for after a three-match winless streak.

Bayern bounced back in emphatic style at the Allianz Arena with winger Arjen Robben in outstanding form.

Goals by Thomas Mueller and Joshua Kimmich put Bayern ahead before Luciano Narsingh netted for Eindhoven before the break.

But Bayern dominated the second-half with Robert Lewandowski putting them 3-1 up before Robben, who had set up two of their goals, added the fourth.

Bayern chairman Karl-Heinz Rummenigge had branded their attitude in Saturday’s 2-2 draw at Frankfurt as “unacceptable”, but Ancelotti was pleased with his side’s response against PSV.

“That was the reaction I expect from the team, the attitude was good, we learnt our lessons from Frankfurt,” said the Italian, who had won his first eight games in charge before the Madrid defeat.

“We very happy to have Manuel Neuer,” Ancelotti added after the Germany goalkeeper pulled off a string of good saves to deny Eindhoven’s attack.

Bayern face PSV away in a fortnight, then travel to face Russian side Rostov before hosting Atletico in their final group match on December 6 in a game likely to decide who wins the pool.

“We played well, but we have to give our best in the next few games to make sure we play Atletico for first place,” warned Ancelotti.

Bayern has six points, three behind group leader Atletico Madrid, which won 1-0 in Rostov. PSV and FC Rostov have one point each.

In Rostov, Yannick Ferreira Carrasco fired in the winner shortly after the hour mark for Atletico, last season’s runner-up.