Every top tier club has someone (usually a small department) for this side of the game these days, it's the kind of thing that gets played up when we're winning. To be fair, almost everything gets played up when we're on a winning run, it's a load of garbage. It's the same in all lines of work.
Remember reading Ledley King's autobiography some time back and when he was talking about Hoddle's management, there was a guy called John Syer - John 'The Head' - whose job was the same, prep them mentally, try to gain that extra few percent, they were already trying things like group visualisation, yoga, one on one counselling sessions even back then. Hoddle was one of the English game's more progressive coaches, bit of a shame how his management career panned out at the end.
For all we know, Peters could still be brought in, do a good job, if the players lack quality or the manager asks ill suited work from his players, we'll still do poorly.