Lazio president Lotito attracted the ire of their fierce rivals by claiming they would not win the title this season after Sunday's 2-2 draw between the two Rome clubs.
Lotito is also reported to have suggested that Roma director Mauro Baldissoni should learn to keep the "club's books in order" - a reference thought to be aimed at the fact Roma remain under investigation regarding their compliance with UEFA's Financial Fair Play regulations.
And Pallotta has now waded into the row by criticising Lotito and stating he would be willing to "educate" his counterpart on Roma's sound financial footing.
"Lotito continues to make foolish and ignorant statements about our club's economics," Pallotta said in a statement published on Roma's official website.
"Next time I come to Rome I will attempt to educate him on our strong and profitable financial position as I would speak to a young child [speaking slowly with as many one syllable words as possible].
"If he still can't figure it out, I give it up."