Killie followed two draws in games they had largely controlled with a 2-1 home defeat by Hibernian on Saturday, despite being deservedly ahead at half-time.
Liam Craig twice capitalised on poor defending to leave Killie still looking for their first victory under Johnston ahead of the second-round clash at Rugby Park.
Johnston said: "Obviously we were disappointed but we can take a lot of confidence from the display.
"The negative part is losing goals and getting beaten. The goals we did lose were really soft and we have got to improve on that. We have got to be a bit more clinical in the final third.
"It's important we start getting wins. It's not good enough just having nice performances. You have got to turn them into results."
Alex Neil's Hamilton have had no problems getting wins as they sit on nine points after three games in the Championship.
Johnston said: "They are playing with a lot of confidence just now. They are top of the Championship for a good reason - they are playing good football, good attacking, scoring a lot of goals. We know it's going to be a really hard game.
"They have got a lot of good players. I saw them a few weeks ago against Raith Rovers. They are really good in the middle of the park, play good football.
"They are really dangerous up front with the young boy (James) Keatings who was at Celtic. So we know how much of a threat it's going to be.
"Hamilton have a good philosophy, the way they try to pass the ball. They have just continued that by bringing Alex in, and it's paying off for them."