United survived a scare in the last round against Division One Ross County, with goalkeeper Steve Banks outstanding during the match and again in the penalty shootout. Last season the Tangerines edged out Partick Thistle with a controversial goal from Damian Casalinuovo, who is now at Hamilton, and went on to lift the cup.
Houston said: "We could quite easily be out of the cup, let's be honest about it. We missed the first penalty in the shootout against Ross County and had to rely on Stevie Banks and other guys to get us through. The margins were so fine and County could have been in the hat instead of us. We rode our luck and got a break but sometimes in cup competition that's what you need to do."
He added: "Every team who has won a cup or done well in one would probably look back to a moment in a certain game and say it proved pivotal for them.
"Last season it was Damian Casalinuovo's goal at Partick Thistle or David Robertson's winner against Rangers - those two moments played a big part in us winning the cup.
"Maybe getting past Ross County on penalties will prove to be one of those.
"But Hamilton will be a massive test and I will be warning the players they can't afford to give teams chances.
"I think we have improved since we played County, we've had a couple of decent results, and I'd love us to continue that improvement this weekend."
Source: PA
Source: PA