The Saddlers – after a summer revamp, bringing in Matt Taylor as head coach – get the new campaign started at Tranmere on Saturday.
And Pomlett, speaking during a Q&A session with supporters at the Banks’s Stadium, is hoping for much better in 2021/22 after ending up 19th last term.
“My vision, really, hasn’t changed. I am very dissatisfied to be the chairman of a League Two football club,” he said.
“I inherited one and I do not want to be one for very long. Jamie (Fullarton) knows that, Stefan (Gamble) knows that, Matt (Taylor) knows that. I want us to get promotion as soon as possible.
“I’m not going to say we’ve got to get promotion this year or we’ve failed.
“But I want us to be an awful lot better than we were last year, and I’m pretty confident we will be.”
Pomlett, who also reaffirmed his desire for Walsall to become a sustainable Championship club in the future, added: “I am looking for us to be in League One, at least, fairly soon.
“They know what the timescales are but I won’t put them under any more pressure.”