The present paper studies online energy management for smart microgrids with the presence of renewable energy resources and energy storages. For the problem at hand, the recent popular approach relies on the Stochastic Dual subGradient (SDG) method. Although SDG enjoys efficient implementation and provable convergence, it generally requires the battery capacity O(1/μ) to guarantee an O(μ)-optimal solution. To overcome this limitation, we develop an Online Learning-Aided Management (OLAM) scheme for energy management, which incorporates the statistical learning advances into realtime energy management. To facilitate real-time implementation of the proposed scheme, the alternating direction method of multipliers (ADMM) method is also leveraged to solve the involved subproblems in a distributed fashion. It is analytically established that the proposed OLAM incurs an O(μ) optimality gap, while only requiring the battery with capacity O(log2(μ)√μ). Numerical tests corroborate that OLAM incurs slightly lower average cost than that of SDG, when requiring battery with significantly lower capacity.