Recent advancements in Large Language Models (LLMs) and multimodal counterparts have spurred significant interest in developing web agents -- AI systems capable of autonomously navigating and completing tasks within web environments. While holding tremendous promise for automating complex web interactions, current approaches face substantial challenges due to the fundamental mismatch between human-designed interfaces and LLM capabilities. Current methods struggle with the inherent complexity of web inputs, whether processing massive DOM trees, relying on screenshots augmented with additional information, or bypassing the user interface entirely through API interactions. This position paper advocates for a paradigm shift in web agent research: rather than forcing web agents to adapt to interfaces designed for humans, we should develop a new interaction paradigm specifically optimized for agentic capabilities. To this end, we introduce the concept of an Agentic Web Interface (AWI), an interface specifically designed for agents to navigate a website. We establish six guiding principles for AWI design, emphasizing safety, efficiency, and standardization, to account for the interests of all primary stakeholders. This reframing aims to overcome fundamental limitations of existing interfaces, paving the way for more efficient, reliable, and transparent web agent design, which will be a collaborative effort involving the broader ML community.