Brendan won the FA Cup here as well. He very nearly qualified for the Champion's League twice with a traditionally non-top 6 side.
Get it into your head that Ange won't be competing in the Premier League with Celtic, he'll be competing with players of a much higher quality, with a much bigger budget, significantly better facilities, etc.
Against higher quality players and managers too, of course, but it's not written anywhere that because a manager comes from Scotland or Japan or wherever, they're automatically incapable of bridging that gap.
No Premier League manager was a Premier League manager before first becoming a Premier League manager.