They're unlikely to reconsider mate, sorry. Don't beat yourself up, thousands of people don't get into their top choice uni and go on to have a great time at another institution.
I'd imagine if they feel other people have stronger PS it could mean that they had more impressive super curricular activities (reading, courses, work experiences), or it could have just been that the way they chose to structure it was more in line with what Manchester specifically look for. Something to keep in mind incase you decide to reapply