The coach did not include Best in his squad for the Republic's recent Euro 2012 qualifiers, citing the frontman's lack of work rate as a reason for his exclusion.
The 25-year-old has won six caps for his country, all under Trapattoni, but has not been selected since pulling out of the squad with an ankle injury which required surgery in May.
Best has been busy winning over an initially dubious Toon Army in the Premier League, and three goals already this season have helped.
That form has prompted Magpies boss Pardew to invite Trapattoni to check out the hitman in the flesh.
He told the Shields Gazette: "I was a little bit disappointed with the manager's comments, because I thought they were a little bit unfair.
"He's got very good strikers, Trapattoni, - make no mistake about that. But to question Leon's work rate, I think, was unfair. I'll tell him that if I ever see him.
"I think he should perhaps come and have another look at Bestie. He might change his mind. I think Leon Best's playing as well as any striker in that Irish squad."