A fee believed to be £7.1million was agreed between the clubs - as well as personal terms. However Ba, 25, who needed knee surgery last summer, has now returned to Germany although Pulis refused to divulge what the problem was.
Speaking after the 2-0 victory against Bolton, Pulis said: "I am desperately disappointed. You look at him and he has a tremendous scoring record. We have been over to watch him three or four times. Everyone has come back with good reports. But we have to put the club first and I understand that."
Pulis, however, hinted the deal could still be resurrected.
"It might be. You don't know, " he said. "The deal we agreed was a great one for the club. It was within our budget, which was really important. There was no problem with the negotiations and the kid wanted to come to Stoke which was brilliant."
Pulis was delighted with the manner of the victory which came thanks to goals from Danny Higginbotham and Matthew Etherington (penalty) either side of half time. Higginbotham scored at the back post while Etherington doubled the lead with a spot kick after being tripped by Zat Knight.
"We enjoy what we do and the players work tremendously hard," Pulis said. "It was a big game for us and I was really pleased with that performance.There are a lot people looking over their shoulders this year. It is such an unusual table, not just at the bottom but the top as well."
Bolton boss Owen Coyle rounded on Knight for flooring Etherington, which effectively put the match out of sight.
Coyle said: "It was a poor penalty for us to give away. Zat Knight has been outstanding but he knows he should have stayed up. Etherington was on his weaker foot and sometimes you have to recognise these situations. Jussi (Jaaskelainen) nearly saved the penalty but we found ourselves 2-0 down.
"We kept going forward and getting in dangerous positions but their keeper made a couple of good saves and we couldn't get that elusive goal to get us back in the game."