It is a practical research topic how to deal with multi-device audio inputs by a single acoustic scene classification system with efficient design. In this work, we propose Residual Normalization, a novel feature normalization method that uses frequency-wise normalization % instance normalization with a shortcut path to discard unnecessary device-specific information without losing useful information for classification. Moreover, we introduce an efficient architecture, BC-ResNet-ASC, a modified version of the baseline architecture with a limited receptive field. BC-ResNet-ASC outperforms the baseline architecture even though it contains the small number of parameters. Through three model compression schemes: pruning, quantization, and knowledge distillation, we can reduce model complexity further while mitigating the performance degradation. The proposed system achieves an average test accuracy of 76.3% in TAU Urban Acoustic Scenes 2020 Mobile, development dataset with 315k parameters, and average test accuracy of 75.3% after compression to 61.0KB of non-zero parameters. The proposed method won the 1st place in DCASE 2021 challenge, TASK1A.