Semi-invasive fault injection attacks are powerful techniques well-known by attackers and secure embedded system designers. When performing such attacks, the selection of the fault injection parameters is of utmost importance and usually based on the experience of the attacker. Surprisingly, there exists no formal and general approach to characterize the target behavior under attack. In this work, we present a novel methodology to perform a fast characterization of the fault injection impact on a target, depending on the possible attack parameters. We experimentally show our methodology to be a successful one when targeting different algorithms such as DES and AES encryption and then extend to the full characterization with the help of deep learning. Finally, we show how the characterization results are transferable between different targets.