Boss Brian Rice wants Hamilton to make a long-awaited impact in the William Hill Scottish Cup this season.
The Lanarkshire side start the competition with a home tie in the fourth round, against Edinburgh City on Saturday.
Major cup competitions have not been kind to Accies over the years, with two losing Scottish Cup final appearances in 1911 and 1935 their high watermark in the tournament, and the latter year also representing their last appearance in the semi-finals.
However Rice, who was assistant to John Hughes when Falkirk reached the final in 2009 only to be beaten 1-0 by Rangers, wants Hamilton to start making amends as they prepare to face a side who are second to Cove Rangers in the table.
He said: "I am always one to talk about performance but in a cup tie it is about winning.
"I think it is maybe time that Hamilton tried to have a cup run.
"We got through the group stages of the Betfred Cup and got beat 1-0 by Kilmarnock in extra time.
"But the Scottish Cup has always been a massive thing for me.
"I got to the final with Falkirk with Yogi (Hughes), when we played Rangers.
"It was everything you dream of. You start out in January, as we do, and you want to get through this round and then you are waiting on the draw being made and it is great.
"There are only two trophies you can win. Realistically you can't win the league, Celtic and Rangers will predominantly win the league.
"So it is a chance for a club to get to a final and get a wee bit of success. Why not us?
"I don't there is any reason why any team shouldn't have a cup run. It is on the day and that is the good thing for me.
"We all want to be there at Hampden in May. We don't want to be there as fans, watching it on the telly abroad, we want to be part of it."
The former Hibernian, Nottingham Forest and Falkirk midfielder will welcome a familiar face to Hamilton.
He said: "It's my first Scottish Cup tie (with Hamilton) and it is funny it comes against Edinburgh City, where Jim Jefferies is.
"Jim is the director of football and obviously I know him really well.
"He brought me back to Scotland from England and someone I have kept close contact with for many years and a man I greatly respect.
"I have seen him at the games, I have been to watch Edinburgh and have been picking his brains about a lot of things so it will be good to see him again."
