Network Function Virtualization (NFV) has attracted a lot of attention in the telecommunication field because it allows to virtualize core-business network functions on top of a NFV Infrastructure. Typically, virtual network functions (VNFs) can be represented as chains of Virtual Machines (VMs) or containers that exchange network traffic which are deployed inside datacenters on commodity hardware. In order to achieve cost efficiency, network operators aim at minimizing the power consumption of their NFV infrastructure. This can be achieved by using the minimum set of physical servers and networking equipment that are able to provide the quality of service required by the virtual functions in terms of computing, memory, disk and network related parameters. However, it is very difficult to predict precisely the resource demands required by the VNFs to execute their tasks. In this work, we apply the theory of robust optimization to deal with such parameter uncertainty. We model the problem of robust VNF placement and network embedding under resource demand uncertainty and network latency constraints using robust mixed integer optimization techniques. For online optimization, we develop fast solution heuristics. By using the virtualized Evolved Packet Core as use case, we perform a comprehensive evaluation in terms of performance, solution time and complexity and show that our heuristic can calculate robust solutions for large instances under one second.