Accies have been tipped for relegation, despite finishing seventh and tenth in the last two seasons.
"When you look at the size of the club and the budget we work with, we are the smallest club," said Canning, 34.
"Logic would say that the smallest club with the smallest budget will be the team that struggles the most, but it's up to us to prove people wrong again."
Player-manager Canning - who will be in the dugout for Saturday's league opener against Rangers following surgery to his jaw - is hopeful of making more additions to his squad.
Goalkeepers Remi Matthews and Gary Woods, defenders Jack Breslin, Jordan McGregor and Georgios Sarris and midfielder Massimo Donati have all been recruited so far.
"We're trying to add as much experience as we can and we've got another couple to try and bring in, if we can get them," said Canning.
"It's now just a case of adding the right players who will improve the starting XI.
"We're looking for a striker, still another centre-back and potentially a right-back as well."
Hamilton travel to face Mark Warburton's Rangers with a number of players unavailable.
Danny Redmond, Scott McMann, Gramoz Kurtaj, Jesus Garcia Tena as well as Canning are all ruled out with injury, however Danny Lyon and Eamonn Brophy could be in contention for a return to the first team after training this week.
Michael Devlin will lead out Hamilton in front of a sell-out crowd at Ibrox after taking over the captaincy from departing goalkeeper Michael McGovern.
Canning believes Devlin, aged just 22, sees captaincy as a natural progression for his fellow defender.
"He's a vocal character, he talks and organises and he conducts himself well," added Canning.
"He's the right type of ambassador for the club and I think he'll do a good job."
Hamilton Academical boss Martin Canning has challenged his players to upset the odds in this season's Premiership.