This paper presents an analysis regarding an influence of the Distance Metric Learning (DML) loss functions on the supervised fine-tuning of the language models for classification tasks. We experimented with known datasets from SentEval Transfer Tasks. Our experiments show that applying the DML loss function can increase performance on downstream classification tasks of RoBERTa-large models in few-shot scenarios. Models fine-tuned with the use of SoftTriple loss can achieve better results than models with a standard categorical cross-entropy loss function by about 2.89 percentage points from 0.04 to 13.48 percentage points depending on the training dataset. Additionally, we accomplished a comprehensive analysis with explainability techniques to assess the models' reliability and explain their results.