Scheduling real-time applications modelled as directed acyclic graphs on heterogeneous distributed platforms is known to be a challenging as well as a computationally demanding problem. This article deals with the design of an efficient scheduler for executing a real-time task graph on a distributed platform consisting of a set of fully connected heterogeneous processors. The objective of the scheduling strategy is to minimize a generic penalty function which can be amicably adopted toward its deployment in various application domains such as real-time embedded systems, cloud/fog computing, industrial automation and IoTs, smart grids, automotive and avionic systems, etc. We have first encoded the problem as a constraint satisfaction problem and then developed an efficient list-based heuristic scheduling algorithm called Penalty-aware REal-time Scheduler for Task graphs on heterOgeneous platforms (PRESTO), to generate a minimal penalty deadline-meeting static schedule. The generic efficacy of PRESTO is exhibited through extensive simulation-based experiments using standard benchmark task graphs. The practical applicability of PRESTO in diverse scenarios have further been exhibited by using the scheme in two different real-world case studies, the first of which relates to automotive embedded systems, while the second is in the domain of fog computing.