Goalkeeper Michael McGovern believes Hamilton can go on to win the League Cup but realises they face a tough match against holders Aberdeen.
"I don't think we're favourites with Aberdeen being at home and being such a big club," said McGovern ahead of Wednesday's quarter-final at Pittodrie.
"But, if we give our maximum, we know we can get a result.
"So-called smaller clubs have won the cup recently, so there's no reason why we can't go on to win it."
Kilmarnock and St Mirren lifted the League Cup in 2012 and 2013 respectively, while Inverness CT reached their first major final last season, only to lose out on penalties to the Dons.
Accies' 11-game unbeaten run came to an end with a 2-0 loss at Dundee on Saturday.
But the Lanarkshire side remain on top of the Premiership and were 3-0 winners at home to Aberdeen earlier this month.
"The players are positive and that comes from getting results," McGovern, 30, told BBC Scotland. "When you get a taste, you just want to get on and get as many wins as you can.
"We're very well organised. The manager has us well drilled and we have really talented players going forward, so we have the ingredients for a good team.
"I'm surprised we are top of the league but I'm not surprised we are doing well."
McGovern, capped once by Northern Ireland, was signed as a free agent by Alex Neil over the summer after three years with Falkirk and has conceded nine goals in 14 games this term.
"A lot of the success is down to the manager," he added. "I've been thoroughly impressed. he sets high standards and that sets the tone for the rest of the lads."
Hamilton, who have been Scottish Cup runners-up twice, have never contested a League Cup final.