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Clark watched his side lose 4-0 to Hearts at Tynecastle and said the scoreline could have been worse.
His squad is debilitated by injuries and the Killie boss believes he must add fresh faces next month to pull his team out of "the rut" they are in.
"It just highlights that I've got to change things in the January window to make us stronger," Clark said.
Kilmarnock are without a win in five Premiership games, and have won only one of their last nine.
Clark does not expect to have any of his injured players available before Saturday's game against Partick Thistle.
"We need to work really hard on Thursday and Friday on nailing down what we're going to do," he said. "I have to find a solution either with the formation or personnel.
"It's a huge game for us on the 31st of December. We need as many points from the teams around us because we're getting heavy defeats from the top six.
"It's one before a significant break and we have to be right up for it.
"We're in a rut, we've been struggling the last two games and we've shown that the injuries have taken their toll.
"We'll need to do something significantly different on Hogmanay against Partick Thistle to make sure we get a positive result because [in] the last two performances we've capitulated and that's been tough to take.
"We're down to the bare bones and we need these important players back as soon as possible, but I don't think that's going to happen before the weekend."
Hearts grew in confidence against Kilmarnock, after suffering for a spell when the opening goal-scorer, Callum Paterson, was stretchered off. The full-back and Prince Buaben, who was taken off injured in the second half, will be assessed by the club's medical staff before Friday's visit of Aberdeen to Tynecastle.
Once Arnaud Djoum scored a second goal just before half-time, Hearts took command of the game. Jamie Walker scored twice after the interval, and the home side might have had five if Dario Zanatta had not missed a penalty in the final minute of the game.
The victory was Ian Cathro's first, in his fourth game since succeeding Robbie Neilson as head coach. He said he was satisfied with the performance but also keen for the team to improve in certain aspects of their game.
"It's satisfaction more than relief," Cathro said. "That just stems from the fact that the players have worked very well.
"We've made small improvements in their play, some things have changed, but the biggest factor was that everybody was asked to give more of themselves, on their playing and leadership qualities, and that was evident throughout the game.
"Of course, there are aspects of our play we will always want to improve and some small errors here and there, but we managed to deal with our mistakes better and that's going to be a big factor in a lot of the games.
"When we could get started and control some of the play we also managed to do that at times as well. Overall a positive feeling, in the knowledge there are things we can do better."
Kilmarnock manager Lee Clark admits he needs to quickly find the answers to his team's struggling form.