Manager Angelo Alessio has warned "there's no reason to be complacent" as Kilmarnock look to complete a Europa League win over Connah's Quay Nomads.
The Scottish Premiership side hold a 2-1 lead after the first leg against the Welsh Premier League runners-up.
But they needed to come from a goal behind in Rhyl and face a side who have won their last two away games on Scottish soil.
"We have to play better than last week," Alessio said.
The carrot for the winners is a second qualifying round meeting with Partizan, who finished third in last season's Serbian SuperLiga and won their national cup for a record seventh time by beating league champions and city neighbours Red Star.
Kilmarnock remain short of numbers, having only made two summer additions after a large section of the squad departed along with Scotland-bound manager Steve Clarke.
Both former Roda midfielder Mohamed El Makrini and on-loan Juventus goalkeeper Laurentiu Branescu were on the bench in Wales, while Alex Bruce is ineligible despite signing a new contract on Wednesday.
Kilmarnock, whose highest league finish since 1966 ensured a return to Europe after an 18-year hiatus, have only won four of their last eight home ties in European competition.
They will be looking to avoid a repeat of their 1970 Fairs Cup experience against Coleraine, when the Northern Irish part-timers shocked their hosts 3-2 at Rugby Park after a 1-1 draw in the first leg.
Connah's Quay's Scottish manager, Andy Morrison, will be reminding his side that they have a good record in Scotland.
They won away to Falkirk and Queen's Park last season on their way to giving Championship winners Ross County a tough test before losing the Scottish Challenge Cup final 3-1 in Inverness.
"We know we need to stay in the game and keep it as tight for as long as we can before we actually show our hand and maybe change things round," Morrison said.
"We've looked at certain things this week. I think the two or three times that we did actually get in their box we always looked like we were going to score.
"So it's about how much emphasis we put on trying to get in there and how that leaves us open at the back, as the higher you go and the better players you play against they'll punish you, they'll make the right decision."