Segmenting brain tumors is a critical task in medical imaging that relies on advanced deep-learning methods. However, effectively handling complex tumor regions requires more comprehensive and advanced strategies to overcome challenges such as computational complexity, the gradient vanishing problem, and variations in size and visual impact. To overcome these challenges, this research presents a novel and computationally efficient method termed lightweight Inception U-Net (LIU-Net) for the accurate brain tumor segmentation task. LIU-Net balances model complexity and computational load to provide consistent performance and uses Inception blocks to capture features at different scales, which makes it relatively lightweight. Its capability to efficiently and precisely segment brain tumors, especially in challenging-to-detect regions, distinguishes it from existing models. This Inception-style convolutional block assists the model in capturing multiscale features while preserving spatial information. Moreover, the proposed model utilizes a combination of Dice loss and Focal loss to handle the class imbalance issue. The proposed LIU-Net model was evaluated on the benchmark BraTS 2021 dataset, where it generates remarkable outcomes with a Dice score of 0.8121 for the enhancing tumor (ET) region, 0.8856 for the whole tumor (WT) region, and 0.8444 for the tumor core (TC) region on the test set. To evaluate the robustness of the proposed architecture, LIU-Net was cross-validated on an external cohort BraTS 2020 dataset. The proposed method obtained a Dice score of 0.8646 for the ET region, 0.9027 for the WT region, and 0.9092 for the TC region on the external cohort BraTS 2020 dataset. These results highlight the effectiveness of integrating the Inception blocks into the U-Net architecture, making it a promising candidate for medical image segmentation.