Magpies boss Pardew did not feel that Ba needed to prove anything to the Potters whilst Pulis concurred, pointing out the reasons why the club did not pick him up from West Ham United.
"No I don't think so," Pardew told Sky Sports 1.
"Demba's played like that all year. He's been brilliant for us. He's a great player who doesn't miss a day's training. I knew of him because of my connections at West Ham and I was very confident to bring him here."
Stoke declined the offer to purchase Ba because they were worried about the condition of one of his knees but Pulis, who also rubbished claims he had something to prove, was not ruing the decision even though the Senegalese attacker has scored eight goals in nine appearances so far this term.
"No, he's scored enough goals without having to come here (with something to prove)," he said. "People know about him.
"When we were going to sign Demba the price tag was £9million and the medical people, who are brilliant at this football club, thought it would be too much of a risk.
"Going somewhere on a free transfer is a different option than paying £9million for what the medical people had seen and we thought it'd be too much of a risk."