In a night of high drama at McDiarmid Park Thursday night, the Perth side were knocked out of the Europa League qualifiers on penalties by Minsk after squandering their 1-0 first-leg lead.
While one school of thought suggests Saints might be downbeat for the Scottish Premiership clash with Killie, Johnston is confident they will be looking to make amends.
He said: "I am sure they will be desperate to make up for that, I don't think it will affect them too much.
"Obviously the game went to extra-time as well so we will need to make sure we play at a high tempo.
"The half-hour extra can take it out of a player plus, it was a midweek game but I am sure the manager will have them fired up and make sure there is a reaction.
"I have seen them three times this season and they have done unbelievably well.
"They are solid, they don't lose goals, they are aggressive in the middle of the park with good experience.
"And look at their front players, they have goals all over the pitch."
The Ayrshire side are looking to get their first points on the board after losing their league opener 2-1 at Aberdeen last week.
The former Queen of the South boss said: "We didn't have a great record at home last year so it would be good to start with a win this season.
"We didn't deserve to win the game at Aberdeen so we need to improve as a team.
"We have really good front players in Kris Boyd and Paul Heffernan and we need to create chances for them."
Johnston admitted that Celtic defender Jackson Irvine, 20, is on his wanted list but does not expect any new faces in before the visit of Saints.
He said: "We are still trying to get people in but I don't think we will have anyone in place for the weekend.
"Jackson Irvine is definitely one we are interested in but nothing has been sorted out yet.
"It won't be done by Sunday, I think he is playing with Celtic in Dublin."