Short answer: No, don't put this on your resume.
Long answer: Just because you were let go during the trial period, due to slower than normal adaptation to the job, doesn't necessarily mean you're bad at what you do. Maybe you just take longer to grasp all the ideals that the company has for their employees. This can lead to you being let go, as you are not "perfect" in their eyes.
Now, knowing that yourself, doesn't mean everyone will see it that way when you walk into an interview. Even if you explain what happened, they might just assume you're putting yourself in a positive light instead of telling them what really happened. I would say leave the job off your resume and just go from there. Build your resume up on your strengths and past employment that you performed well in. The people who read your resume will only see that you lasted in your previous job for a month, and they'll wonder why, possibly might kill your chances of getting an interview.
Again, don't get down on yourself. Each company has different expectations of their employees, some expect you to be a pro within a week, some expect it's going to take longer to get settled in and they understand things can take time, especially for a new employee. Just keep working hard and keep your resume focused on the good.