Ba would have joined the Potters in January had he not failed a medical, leaving the Magpies to nip in to buy the Senegal international and he has repaid them with a superb start to the season with Monday night's efforts taking him to eight goals in five games.
Of the Potters fans who made their displeasure known, Ba said: "If they want to boo they should boo their board."
He added: "Today I am very happy to score a hat-trick here because it is a place you come and struggle.
"It's very important when you have strikers who can run and defend.
"Today we did our best but the team at the back were very strong."
Ba refused to look too far ahead despite Newcastle's position in the table, saying: "We are just in the first 10 games so it's a long way to go."
Newcastle manager Alan Pardew also paid tribute to Ba and dismissed Tony Pulis' fears over the player's physical condition, which led the Potters boss to eventually not sign him.
Pardew though denied the player had a point to prove and told Sky Sports 1: "Demba has played like that all year.
"I knew of him because of my connections at West Ham, I was very confident of bringing him here."
The Magpies boss praised his side's defensive qualities in the face of Stoke pressure, saying: "The resilience showed a different side to us, you don't have 22 points without different sides.
"They (Stoke) are a top team and will finish in the top 10."
The former West Ham boss was keeping his feet on the ground despite being third.
"We are coming into a tough run of games but we are in a really good position."
Pulis defended his decision not to sign Ba, telling Sky Sports 1: "When I was looking at him the price tag was £9million and the medical people here - who are brilliant - thought that would be too much of a risk.
"Being on a free transfer is a different matter."
He admitted he was "desperately disappointed" with tonight's result and believed his side's defence was not up to its usual standard.
"The first two goals are poor.
"On the first the lad is offside from the goalkeeper's kick but from that point on the defending was very poor from us.
"We got the goal back and you think we can step on it but the penalty he gives them kills the game.
"I thought we had the ascendancy in lots of respects.
"But fair play to Newcastle."