Few-shot Knowledge Graph (KG) Relational Reasoning aims to predict unseen triplets (i.e., query triplets) for rare relations in KGs, given only several triplets of these relations as references (i.e., support triplets). This task has gained significant traction due to the widespread use of knowledge graphs in various natural language processing applications. Previous approaches have utilized meta-training methods and manually constructed meta-relation sets to tackle this task. Recent efforts have focused on edge-mask-based methods, which exploit the structure of the contextualized graphs of target triplets (i.e., a subgraph containing relevant triplets in the KG). However, existing edge-mask-based methods have limitations in extracting insufficient information from KG and are highly influenced by spurious information in KG. To overcome these challenges, we propose SAFER (Subgraph Adaptation for Few-shot Relational Reasoning), a novel approach that effectively adapts the information in contextualized graphs to various subgraphs generated from support and query triplets to perform the prediction. Specifically, SAFER enables the extraction of more comprehensive information from support triplets while minimizing the impact of spurious information when predicting query triplets. Experimental results on three prevalent datasets demonstrate the superiority of our proposed framework SAFER.