"In football terms, the difference between a Premiership player and all the other divisions is his mental state, his mental agility or his decision-making process.
"Premiership players' skills are sometimes no greater than players below them in different leagues, but they can play in the Premiership because they can cope better mentally.
"By giving no coaching on that, you undermine the potential of your players.
"In that area, Dr Nesti is one of the best. He is one of the most qualified men I have ever met. He is a magic guy at what he does."
Nesti is an expert in "existential psychology" based at York St John University, but worked with Allardyce for five years at Bolton.
"This country has a far too negative view on psychology. We fall way behind a lot of countries in that respect," added the Newcastle boss.
"It is a very big part of football - the most important part. What goes on between the ears is what makes you as good as you are as a player."
Allardyce added: "I wouldn't tell you if Michael (Owen) has seen him, it is purely confidential between those two people. I cannot breach that confidentiality."