The tracking of citizens' reactions in social media during crises has attracted an increasing level of interest in the research community. In particular, sentiment analysis over social media posts can be regarded as a particularly useful tool, enabling civil protection and law enforcement agencies to more effectively respond during this type of situation. Prior work on sentiment analysis in social media during crises has applied well-known techniques for overall sentiment detection in posts. However, we argue that sentiment analysis of the overall post might not always be suitable, as it may miss the presence of more targeted sentiments, e.g. about the people and organizations involved (which we refer to as sentiment targets). Through a crowdsourcing study, we show that there are marked differences between the overall tweet sentiment and the sentiment expressed towards the subjects mentioned in tweets related to three crises events.