Even though Killie need just one point to ensure their survival in the Scottish Premiership, Johnston believes they must not try to settle for a draw.
Killie were boosted ahead of this weekend's crucial game by beating St Mirren 1-0 at Rugby Park on Wednesday when Kris Boyd netted the only goal.
And Johnston admits: "It's a hard one to approach on Saturday. We know we have to go out there with a similar type of performance, the same sort of tempo we played with tonight and try to get the three points.
"I think it's hard to just play for one point. We've just got to go for it and try to end the season on a high and get the result we need.
"We know it's going to be like a cup final. The Hibs fans will know how vital it is as well and they will get right behind them and there will be a big crowd.
"You could see with our fans tonight, who were fantastic, that it makes a huge difference. I'm sure they will be there in their numbers as well."
Saints boss Danny Lennon has other things on his mind, such as a board meeting involving club chairman Stewart Gilmour and his fellow directors to discuss the manager's future.
Lennon, who is out of contract at the end of the season, said: "I'm not worried about it at all.
"My remit was to make sure this club stayed in the top flight of Scottish football and I've done that.
"I've held up my end of the bargain and also won a national cup. On the whole, we've achieved more than the expectation was.
"But I'm my own biggest critic. I've made mistakes at St Mirren but ones I've learned from. I'm a better manager for it today."