The Bavarians thrashed Sporting 5-0 in Lisbon on Wednesday, but Klinsmann is still aware of the importance of the return leg on March 10th.
"Realistically, you have to say we’re almost through to the quarter-finals," Klinsmann said after the game.
"It’s hard to imagine we’ll let it go wrong now, but we’ll still have to approach the return with the seriousness it deserves."
The former Germany coach was full of praise for his players, stressing that the big win shouldnt let arrogance find its way within the team.
"That was a scintillating display and great to watch, but I’m confident we’ll keep our feet on the ground and not read too much into today’s result.
"We need humility and we need full concentration to get our Bundesliga position sorted out."
Four-time European champions Bayern will be looking to reach their first Champions League quarter-final in two years, after the club only managed to reach the UEFA Cup last season.