Bayern sit top of the Bundesliga and are set to face Bayer Leverkusen in the quarter-finals of the DFB-Pokal next month, but the German champions were held to a goalless draw in Ukraine three weeks ago.
That stalemate leaves Bayern needing a win at the Allianz Arena to book their place in the quarter-finals, but Lahm - set to make his comeback after four months out with a broken ankle - is not getting ahead of himself.
"It is always the goal to win every competition, especially when you are playing for Bayern Munich. But that is tough," he told Perform.
"The Champions League is not a title you can win with no effort. It is a hard competition.
"The most important thing is to win the Bundesliga because you want to stay at the top in Germany, plus it is over a whole season. At the end it is an honest result. You can have a bad day and it will not affect anything.
"In the end the best team in Germany is at the top of the table. That’s the reason why it is the most important thing.
"But of course I want to win the Champions League."
Lahm, along with several of his Bayern team-mates, was part of Germany's World Cup-winning squad last year and has compared the experience to that of lifting the Champions League trophy.
"The feelings are similar," he added. "One is the highest possible achievement you can reach with your club and the other one is the highest possible achievement for a national team. Both are really important.
"I think the realisation of winning the World Cup will only set in after we retire. In our business things go on very fast."
And the quality at Bayern's disposal is not lost on Shakhtar coach Mircea Lucescu.
"We'll be playing against a very strong club," he told UEFA.com. "In my opinion Bayern are the world's strongest football team at the moment.
"They have six world champions among their players, and leading figures like [Franck] Ribery or [Arjen] Robben."
Bayern will be without Xabi Alonso, who was dismissed in the first leg, while Taras Stepanenko returns from suspension for Shakhtar.
