I'll repeat the line.
There's no evidence that in the Premiership, when equalising for other factors, that managers make any positive difference to their team. Ferguson and Wenger being the exceptions. And it's thought that they make their difference through shrewd purchases and sales.
The fact that the vast majority of examples people are citing come before the Premiership era is telling, and not surprising since the differences in money were such back then that managers were more important. Before the Premiership teams split gate receipts, there were no major tv deals or sponsorship deals which created such massive inequality that exists now. And there was no need to have any qualifications to become a manager.
Nowadays with the coaching badges that everyone has to take there's less of a difference between managers. Now that all the backroom teams are full of qualified professionals to deal with every aspect of the game , there's less a manager can and needs to bring to the table - particularly in terms of preparing a team.
You'll most often find that a teams rise coincides with increases in spending on wages and transfers. Which is not the slightest bit surprising.