Objective: This study proposes a computationally efficient method to quantify the effect of surgical inaccuracies on ligament strain in total knee arthroplasty (TKA). More specifically, this study describes a framework to determine the implant position and required surgical accuracy that results in a ligament balanced post-operative outcome with a probability of 90%. Methods: The response surface method is used to translate uncertainty in the implant position parameters to uncertainty in the ligament strain. The designed uncertainty quantification technique allows for an optimization with feasible computational cost towards the planned implant position and the tolerated surgical error for each of the twelve degrees of freedom of the implant position. Results: It is shown that the error does not allow for a ligament balanced TKA with a probability of 90% using preoperative planning. Six critical implant position parameters can be identified, namely AP translation, PD translation, VV rotation, IE rotation for the femoral component and PD translation, VV rotation for the tibial component. Conclusion: We introduced an optimization process that allows for the computation of the required surgical accuracy for a ligament balanced postoperative outcome using preoperative planning with feasible computational cost. Significance: Towards the research society, the proposed method allows for a computationally efficient uncertainty quantification on a complex model. Towards surgical technique developers, six critical implant position parameters were identified, which should be the focus when refining surgical accuracy of TKA, leveraging better patient satisfaction.