Jim Jeffries wants to build on Kilmarnock's impressive start to the season by turning Rugby Park into a fortress.
He said: "Apart from the Old Firm, we have done well at home in the last year of so.
"We've made Rugby Park tough place to come to, as Aberdeen found out in our last match there. We've also beaten Hibs and Hamilton.
"We want to keep it going. Motherwell are still a tough side to beat as they're not too far away from us, then we've got Falkirk and that'll be tough as they're capable of winning away from home if you let them play."
Jefferies knows they need to maintain the high standards they've set so far in this campaign.
He said: "Being in third place is great when you look at it but let's be realistic. Aberdeen are only six points off third, so there's nothing in this league and everyone is capable of beating each other.
"There will be a lot of movement between the top six and bottom because it's so tight.
"Rangers and Celtic don't drop too many points but St Mirren showed you can pick up points against them.
"You look at the fixtures and you can't predict who'll win. People are just guessing as it's just on the day who takes their chances.
"As long as we're contesting and trying to make the top six, that'll be a massive improvement.
"That'll be a great platform to go on.
"But I think this team are quietly confident that they can challenge and they've got belief they can prove a few doubters wrong."