Saturday’s 1-0 defeat to St Johnstone means the Rugby Park outfit have now gone seven games without a win.
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Johnston knows the dangers of such a run after watching as results ultimately cost three of his managerial colleagues their jobs this week.
But Johnston - who survived a nightmare run last season which saw his side go 10 games before picking up their first victory - said: “There’s no point worrying about it - if it’s going to happen it will happen.
“It’s all about making sure you are giving your team the best chance of winning. If you look at every manager, whether it is here or elsewhere, you are always under pressure.
“Results dictate if you are going to stay.
“The chairman has been different class but I’m realistic enough to know that we have to be winning games. The guys in the boardroom want to be challenging for the top six and so do I. I’m still ambitious.”
Johnston’s top-six ambitions looked like they were set to be fulfilled after a promising start to the Scottish Premiership campaign.
Six wins from their opening 10 league matches pushed Kille up to joint third by mid-October - but they have now dropped to seventh, while their William Hill Scottish Cup hopes were ended by a 3-0 defeat to Rangers last month.
Without last season’s top scorer Kris Boyd, Johnston has also watched the goals dry up too.
The Ayrshiremen have netted just four times during their recent downturn, while shipping 16 at the other end.
The manager, however, believes his side can easily turn things around so long as Killie keep cool heads.
He said: “We’ve not got a striker who will score 20-odd goals a season like Boydy, so it will take goals from all over the park to get us out of this rut.
“Confidence always dips when you start losing a few games and you can see that in our play now.
“But the last few weeks have been much more encouraging. We created a number of chances against St Johnstone but we just need to make sure we are more clinical.
“I heard Frazer Wright talking after the game and he was saying that when they went through a run like this at St Johnstone, they just did not panic.
“That’s something we need to take on board. If you have got the experience to know that if you keep on doing the right things then it will turn.”
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