Segmenting ultrasound images is critical for various medical applications, but it offers significant challenges due to ultrasound images' inherent noise and unpredictability. To address these challenges, we proposed EUIS-Net, a CNN network designed to segment ultrasound images efficiently and precisely. The proposed EUIS-Net utilises four encoder-decoder blocks, resulting in a notable decrease in computational complexity while achieving excellent performance. The proposed EUIS-Net integrates both channel and spatial attention mechanisms into the bottleneck to improve feature representation and collect significant contextual information. In addition, EUIS-Net incorporates a region-aware attention module in skip connections, which enhances the ability to concentrate on the region of the injury. To enable thorough information exchange across various network blocks, skip connection aggregation is employed from the network's lowermost to the uppermost block. Comprehensive evaluations are conducted on two publicly available ultrasound image segmentation datasets. The proposed EUIS-Net achieved mean IoU and dice scores of 78. 12\%, 85. 42\% and 84. 73\%, 89. 01\% in the BUSI and DDTI datasets, respectively. The findings of our study showcase the substantial capabilities of EUIS-Net for immediate use in clinical settings and its versatility in various ultrasound imaging tasks.