Tosun scored both goals for Everton as they secured a 1-2 away win over Stoke on Saturday. The victory was only Everton's second win away from home in this season of Premier League football.
The brace means that the Turk now has four goals in seven games, and is seemingly the solution to Everton's goalscoring problems.
Many people had criticised Allardyce for not putting the striker in the team earlier, but speaking after the game the Everton manager backed his decision to introduce the player slowly, claiming that critics don't understand the situation.
"I think his confidence is gained by us taking him out early doors when everyone was going: 'Why aren't you playing him?'"Allardyce stated.
"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."
Allardyce went on to praise Tosun's contribution to the game. "We had a goal scorer at one end who was clinical and turned the game in our favour with the first goal," he said. "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."