Bioacoustics, the study of animal sounds, offers a non-invasive method to monitor ecosystems. Extracting embeddings from audio-pretrained deep learning (DL) models without fine-tuning has become popular for obtaining bioacoustic features for tasks. However, a recent benchmark study reveals that while fine-tuned audio-pretrained VGG and transformer models achieve state-of-the-art performance in some tasks, they fail in others. This study benchmarks 11 DL models on the same tasks by reducing their learned embeddings' dimensionality and evaluating them through clustering. We found that audio-pretrained DL models 1) without fine-tuning even underperform fine-tuned AlexNet, 2) both with and without fine-tuning fail to separate the background from labeled sounds, but ResNet does, and 3) outperform other models when fewer background sounds are included during fine-tuning. This study underscores the necessity of fine-tuning audio-pretrained models and checking the embeddings after fine-tuning. Our codes are available: https://github.com/NeuroscienceAI/Audio\_Embeddings