Sometimes little Mrs. Phillips worried, and good-natured Mr. Phillips laughed and "poohed" at her fancies.
Her father pshawed and poohed a good deal when he had finished the billet, and examined the seal.
He poohed at it, said it was impossible; but upon their insisting, he at last brought them before the old gentleman.
1590s, "a 'vocal gesture' expressing the action of puffing anything away" [OED], first attested in Hamlet Act I, Scene III, where Polonius addresses Ophelia with, "Affection! pooh! you speak like a green girl, / Unsifted in such perilous circumstance. / Do you believe his tenders, as you call them?" But the "vocal gesture" is perhaps ancient.