Goals from Albert Luque and young striker Andy Carroll ensured victory for the Magpies but Dyer caught the eye with an energetic display in the second half.
He made one thrilling 60-yard dash and later put the ball in the net with a cheeky backheel - an effort that was immediately chalked off for offside - but the former Bolton boss insists he is still likely to be leaving the club due to personal reasons.
West Ham and Tottenham are both being heavily linked with the England man, but no deal is yet off the ground.
"He played very well. But I don't think we can (keep him) for the reasons I gave on Thursday," he said.
"The only way I can see to resolve this is for Kieron to move closer to his family.
"Nobody has come in with the right money yet. Nobody has offered anything like the money we want.
"If they don't come in (with the right offer) then all I can do is sit down with Kieron and see if there's something else we can do.
"We used him for 45 minutes today because we were short of numbers."
One player whose Newcastle career could be going in the other direction is Luque.
He was considered an expensive flop under former boss Glenn Roeder and looked like he would struggle to adapt to the rigours of English football.
But in the absence of injured pair Michael Owen and Shola Ameobi - as well as summer signing Mark Viduka, who is recovering after international duty with Australia - he has been given the chance to impress Allardyce.
He scored twice in the 4-1 win over Celtic and coolly slotted his first-half penalty past Gianluigi Buffon to set the ball rolling against the Turin side.
Although he came off after just half an hour with what seemed to be a minor knock he did enough to impress his boss.
"The only negative thing today was Albert coming off. But he assures me it's just a tightening (of the muscle)."
Asked if Luque could become a fixture this season, he said: "Hopefully, If he can stay fit he could play a part."
Reflecting on a match that saw United outplay their illustrious opponents and end the game with a host of youngsters on the pitch, Allardyce said: "We played well today. It was very important to get a clean sheet.
"I think at time we even played better than we did against Celtic. But I don't want people to get carried away because we've beaten Celtic and we've beaten Juventus."
Juve boss Claudio Ranieri, the former Chelsea manager, insisted Newcastle's superior match fitness was key.
"It was tough and Newcastle were good. But they are at a level where their season is nearly starting and we are not yet.
"Sometimes with our last pass, or with the penalty, we were off or (Shay) Given would make a great save.
"Given was the best player."
But he denied that he would be using his knowledge of the English game to boost his squad while he was in the country.
"Am I looking at players in England now? No. Juventus for now are finished (in the transfer market)."