Robert Lewandowski struck a 19th minute winner on the night.
Flick later said: "I've been told that it's normal against Getafe because they're very good in defence. I'm very proud, they fought for 95 minutes. The fans were fantastic, they realised that we needed them.
"We had one chance and scored and they had another, but they lost.
"In the first half, we didn't maximise our passes and they closed off the spaces for us. But the players fought. I'm proud because we fought with a positive mentality. Today I realised that we need the fans."
On Lewandowski, he said: "For me, he is the best number nine of the last ten years, and his job is in front of goal, in the area... and he does it very well. We surrounded him with players. His goal was great. In the first half, we scored and played with a lot of passes. I am very happy. The victory was possible thanks to the team. We have to continue with the high performance."