Applying for a faculty job without history of external grants I have worked in a research institute (R&amp;D for a parent company) for 10 years after my postdoc. I used to teach occasionally as an adjunct professor. Despite our R&amp;D theme, I have an excellent record of publication (comparable with my peers in terms of quality and quantity; unquestionably good). However, I never applied for external funding, as our research fund was directly provided by the institute.

I applied for some faculty positions but unsuccessful. They didn't give me a detailed feedback but mentioned that a criterion for the job is "demonstrated success in securing external funding".

Should I give up? Because this is something I cannot do anything about it. Unless I assume a faculty position I cannot send research proposals for external funding. And if this is a mandatory condition, I can never assume a faculty position.

I understand that external funding is important for universities, but I wasn't unsuccessful, just didn't need to apply because of my job. I understand that proposal writing might be different but my successful research shows that I can write winning proposals too. I have conducted all my research projects based on initial proposals, but they were internal.
While having a history of external grants is helpful, it is not mandatory. I was in a similar position as you were, and managed to secure several offers. What you need to do is have good answers prepared for these two things:

Why Not?: In my case, as with yours, I was in a research institute, which meant things were supported by large grants that were well beyond my "pay grade" to pursue, and where the priorities for postdocs were producing research and doing the things that kept funders happy, rather than chasing new funding. People were very understanding of these sorts of positions.

How Will This Change?: Given you don't have a track record of getting external funding, you need to be able to articulate how you will go about getting one. Having a clear idea of what mechanisms you'll target, how you'll frame your research that way, etc.

Basically, you need to frame not having grants as a deliberate, strategic choice in your old position that will change in your new one as you become an independent researcher.