The 26-year-old put the Blues ahead in the second half against the 10-man Potters and then headed home the winner following Eric Maxim Choupo-Moting's equaliser, taking his tally for four in three games after being reintroduced the side.
Tosun was handed back-to-back starts following his transfer from Besiktas in January but was then dropped back to the bench as Allardyce and his team elected to work him back in gradually.
"I think his confidence is gained by us taking him out early doors when everyone was going: 'Why aren't you playing him?'," Allardyce said.
"You know, it's the usual rubbish you get from outside the football club. They say: "You pay all that money and don't play him, why not?" That's because they don't know. I do, they don't.
"We wanted to get him fitter, and more used to the players he was playing with. A lot of the training and extra training he's done, especially in Dubai, has paid dividends not only for us but for him and long may it continue.
"I think we deserved to win, with them being down to 10 men and us dominating possession, but they gave us a good fight.
"We had a goal scorer at one end who was clinical and turned the game in our favour with the first goal and when we sloppily gave a free-kick and gave a goal away he pops up with a second which was a wonderful finish and a wonderful cross."