Celtic travel to Rugby Park for the Saturday lunchtime kick-off 10 points adrift of leaders Rangers and behind Motherwell.
Neil Lennon's men have lost five of their last 10 matches in all competitions and Ledley knows they cannot afford another slip-up.
However, the Welshman retains belief Celtic can go on a run with a game in hand to come against Dunfermline at Parkhead on November 23, a date set on Thursday by the SPL.
Ledley, who was promoting the club's October school holiday coaching courses, said: "There's pressure in every game, no matter who you're playing.
"There are a lot of games to go and a lot of points to play for. We have still got to play Rangers three times and we have got a game in hand.
"We need to win that and we need to win on Saturday just to kick-start our season.
"We know we can play a bit better than we are at the moment but hopefully we can find the form, and we have been unlucky with injuries as well.
"We have lost key players but there are no excuses and hopefully we can hit form and get on track.
"Kilmarnock are a good team and play good football so it's going to be difficult. We are going to respect them and play our own game."
Lennon spoke candidly about the team's predicament after their 2-0 defeat at Hearts before the international break, admitting he might have to consider his position if results did not improve.
And Ledley is determined to ensure his manager remains at Parkhead.
"Obviously that's down to the club what they want to do but we are all in it together," the former Cardiff player said.
"We all love working with the gaffer, he is great on the pitch and off the pitch.
"He has helped us a lot considering we are young players.
"Hopefully he can stay here for a long time. He is one of the best managers I have worked under."
Ledley missed the Tynecastle defeat with a groin injury, which also forced him out of international duty.
But he has declared himself fit for the game against Kilmarnock.
"I trained today for the first time in about 10 days and it feels okay so hopefully I'll be involved on Saturday," the 24-year-old said.
"Obviously it's down to the manager if he picks me but hopefully I can last 90 minutes."