Applications requiring low-latency packet processing are challenging for today's network and service management when resources are limited and must be shared. Containers are suitable, but achieving connectivity between containers exclusively in software is unsuitable for low-latency requirements. The impact of network latencies in containerized environments has received comparatively less attention, particularly in comparison to research on virtual machines. This paper analyzes throughput and network latencies in container-based networks on a single host featuring single-root input/output virtualization, Linux Containers, and commercial off-the-shelf hardware. We conduct measurements using a state-of-the-art measurement methodology to identify tail-latency behavior, achieving a resolution of 1.25us. We evaluate a single flow in a line topology with up to 64 containers and a complex topology with 38 flows and 12 container nodes. The experiments demonstrate that pinning interrupt request handlers to non-uniform memory access nodes increases throughput and decreases latencies. Furthermore, we identify data translation lookaside buffer misses, rescheduling interrupts, and soft interrupt floods as critical challenges causing spikes in latencies while isolation remains impossible. Our findings identify bottlenecks for real-time container applications. A comparison with VM measurements shows that containers can achieve latencies up to 60 us lower. We support in this paper, network and service management in deciding on the underlying virtualization technology for packet-processing applications by providing recommendations accordingly.