You put it on your resume, of course.
You had senior management experience. That is awesome. This isn't a time to hide the fact that you are a high achiever who learnt valuable management lessons and who feels that tempered with a team lead role can become a major contributor to the underlying growth of some company. It is the time to sing it.
There is nothing wrong with lacking skills that you had no prior training for. Incidentally, if you know specifically in which areas you were let down, now would be a good time to brush up on those areas. You might as well take something from the experience, amiright?
You last paragraph makes sense too, and can be used as an explanation of why you're wanting a strong team lead role so you can build upon the skills you gained in your time at the other company. I wouldn't quite go so far as to provide explanations on your resume as to why you weren't kept on though.
In the resume just put what you contributed, what you learnt, standard bullet-point stuff.
In the cover letter or in the interview when they will ask, that is when you explain. You might do it by expressing that you are excellent at managing developers and refining requirements and contributing to the overall vision of the company. however, the requirements shifted and both you and the company realised you weren't the right fit. the company came to the realisation that a more experienced manager would be needed. you realised that you needed to consolidate the amazing skills you have in a slightly more junior role to be able to fully realise your abilities. And that slightly more junior role is this tech lead (or whatever role you're applying for).
As an aside, I'm not sure you want to jump back down to tech lead?
unless you didn't have any tech lead experience in the last company i read your question and you've had team lead experience, wouldn't you want to be a dev manager, or something with tech leads reporting into him or her?
Although as noted in the comments, it is understandable to use a familiar role to "collect your bearings" and stabilise before moving up again.