The striker, who has failed to make a lasting impression at Villa Park since his £12m switch from Brentford in 2017, joined Stoke on deadline day in a deal lasting until the end of the season.
He scored his first goal for his new side this weekend, bagging Stoke's second in their 2-2 draw against Derby County.
Hogan told StokeonTrentLive: “Yes, hopefully, if all fits. I was happy to come here, fitted in well and know a lot of the lads from the national team as well.
“It all depends on having a good season, but that's what I plan on doing.
“I've got a lot of people to prove wrong. I've been written off by a lot of people who don't think I'm this and don't think I'm that, that I'm a waste of money and all this.
“They can say what they want. That's what is driving me to do well and I've got a manager who believes in me.
“He is a great guy, a great manager and there are great lads here who want me to do well. It's up to me."