They are never going to give you specific examples of why they let you go and they have no obligation to tell you. So when things are beyond your control you can only really focus on what you can change about your approach to set yourself up to kick ass next time.
The truth of the matter is that 7/10 managers do not know how to manager. They also hate conflict, and they never set clear expectations on what is required of you.
On ANY new job, what you need to do is be assertive in your first week to determine 3 things:
how you manager prefers to be communicated with. This isn't how they communicate with you (necessarily) e.g. they shout at your from their office. Do they like email? IM? Phone? Or for you to knock on the door? Appointment only?
What are their expectations of you. The goal here is to get them to tell you what things they expect (e.g. you need to file x number of reports, or make z number of calls) so that you can tell them that you did x,y,z and you can gauge how you are performing, and who to look at to emulate.
Get them to tell you what their pet peeves are. These will be your areas of conflict. e.g. they hate when people are late, or don't keep them in the loop etc. IF they HATE it when people are late and you're late one day, meet that head on. Go right up to them and say "i know I was late today, it was a one time thing and it won't happen again" They will still be upset, remember how they hate conflict? They likely would have just bottled it up and not said shit, until a dozen of those things pile up and you end up out on your ass.
This will set you up for success in your first few weeks to make a great impression.