David Martindale's side emerged triumphant after a penalty shoot-out win over the Saints at the Tony Macaroni Arena on August 14, after which the Paisley side were hammered 6-0 by Celtic.
However, Jim Goodwin's men have slowly got back on track and the 3-2 win over Aberdeen last week - their first in the league - made it four games unbeaten to move them up into eighth place, and Fraser is keen to keep the momentum going.
Speaking about the cup game, the defender said: "We don't really speak about it as a group but it maybe sticks in players' minds that you went down there a few weeks ago and they knocked us out of the cup.
"You have to have that wee bit inside you that remembers it and hopefully this weekend we can rectify that.
"Before the last game we didn't have a win but now we are four unbeaten. We know it is going to be a tough game but we will try to carry that momentum on."
Livingston defender Jack Fitzwater however says the Lions are a match for anyone at home – proven by their result against Celtic last month.
They now host St Mirren before finishing their first round of cinch Premiership fixtures against St Johnstone, Ross County and Dundee United.
After a particularly difficult opening to their campaign, Fitzwater is determined to get some wins on the board, especially at the Tony Macaroni Arena.
The centre-back said: "The game against Celtic, we put absolutely everything into it. We went again, contained Rangers and then a couple of mistakes gifted them two goals. On Saturday [against Hearts], I just think none of us were at the races.
"This weekend is massive. Before the Celtic game we knew we had a run of fixtures now where we will look to pick up as many points as possible, especially our home games.
"If teams start coming here fearing us before they even get on the pitch, then that's what we have to do, because it gives us a lift and we know we are a match for anyone here."