Hibs averted a fifth consecutive defeat when Scott Robertson netted their first goal of the campaign late in the visit of Dundee United on Saturday but manager Pat Fenlon remains under pressure from fans despite being backed by the board this week.
Killie looked to be heading for their first Scottish Premiership victory at St Mirren Park until goalscorer Kris Boyd was sent off and went on to draw 1-1.
Johnston said: "They will be desperate to pick up points. They're a good team with good players and I'm sure they will be desperate to show everyone they shouldn't be where they are.
"But we have got to start picking up points as well. We have had two draws from the last two games and we should have a lot more points.
"Last Saturday against St Mirren we were in control and Boydy gets sent off. The week before against St Johnstone we created loads of chances and should have won the game as well. We need to start picking up three points."
Johnston signed former Aberdeen midfielder Barry Nicholson and former Falkirk and Dundee striker Mark Stewart in the build-up to the St Mirren encounter but he will not add to his squad before the Hibs clash.
"We are still trying to bring in a couple more but I think that will be last minute and we'll have nobody in place by the weekend," he said.
"A couple of clubs have said they will let players go out on loan but they might have to play some games coming up. Hopefully they will work out.
"When I first came in the majority of the boys were under 20 or over 30. There was only one, at 24, in the middle. It was unbelievable.
"So we are just trying to address that and bring in some boys in the middle age group who have got a wee bit of experience but still got good energy as well."
- Sports & Recreation
- Scottish Premiership
- Dundee United
- Pat Fenlon