"It's a massive game for us and I think it's vital that we get a result even though we'll get two bites at the cherry," said Curtis.
"If we can get something tonight, it should make it easier for us in the return leg on Thursday.
"We're desperate to end the season well and our last two league games weren't bad.
"Now we're in a positive frame of mind and we want to win this competition. We don't care what competition it is, we want to win it."
Swansea are due some success in a tournament they have never won, but they will have to do it without a number of players in tonight's game at least.
A lengthy injury list includes centre-backs Kris O'Leary (knee) and Jason Smith (ankle), striker Steve Watkin (wrist) and young midfielder Lee Jenkins (thigh).
Meanwhile, Merthyr player-boss Keith Walker is hoping to end his long stay in Wales by causing an upset. The centre-back spent 10 happy years at the Vetch after joining the club back in 1989.
But fans' favourite Walker will quit football and return to his native Scotland to start a career in the police force when Merthyr's Premier Cup run comes to an end.
"It's ironic that my last game looks like being at the Vetch," he said.