Bayern Munich edged the Champions League first leg of their play-off tie with Celtic, leading Brendan Rogers to urge his side to leave the return fixture with "no regrets".

Michael Olise fired home a sumptuous opener on the stroke of half-time before Harry Kane doubled the lead for Vincent Kompany's visitors in the second half.

However, Daizen Maeda managed to pull one back for the hosts at Celtic Park with 11 minutes remaining, offering Rodgers' men hope before the second leg in Munich on Tuesday.

The Celtic manager was pleased with the way his team ended Wednesday's clash and called on them to not leave anything to the imagination in Munich.

"The last 25 minutes, we started to press the game, we were more active at the top end of the pitch, and you see what it brought - aggression," Rodgers told TNT Sports.

"Our football starts to come alive, and then we get the goal.

"At 2-1, Bayern Munich are hanging on. That's what we can take from it. We've got one more shot. It's a new level for a lot of the players, they've done absolutely great.

"Let's go and have no regrets and see where it takes us. We've shown we can play football and be a threat.

"We're still right in the tie. With their quality and the number of goals they can score, sometimes these can be out of sight, but that wasn't the case at all."

Kane's finish from Joshua Kimmich's corner proved to be the difference, as the striker scored for the 19th time against Kasper Schmeichel, five more than he has managed against any other goalkeeper.

The Bayern forward also moved onto 46 Champions League goal involvements, with only David Beckham (52) and Wayne Rooney (47) ever managing more among English players in the competition.

Kane acknowledged the Celtic Park atmosphere would always pose a difficult challenge, though lauded Bayern's "special" quality that helped them navigate a boisterous home support.

"[Our performance] was okay. Whenever you win a game like this, you're always pleased because it's not an easy place to come," the England captain told TNT Sports.

"There were definitely areas in the game in which we could have done better, and we'll need to improve for next week, but overall we scored at the right times.

"They put us under pressure at the end, and we had to stay strong, which we did.

"We knew the atmosphere would help them at the start of the game, and they nearly scored after a minute. We had to be patient, we knew we'd have more of the ball.

"Sometimes you need a bit of special quality to open a game like this up."