The migration rate and the level of resentments towards migrants are an important issue in modern civilisation. The infamous EU refugee crisis caught many countries unprepared, leading to sporadic and rudimentary containment measures that, in turn, led to significant public discourse. Decades of offline data collected via traditional survey methods have been utilised earlier to understand public opinion to foster peaceful coexistence. Capturing and understanding online public opinion via social media is crucial towards a joint strategic regulation spanning safety, rights of migrants and cordial integration for economic prosperity. We present a analysis of opinions on migrants and refugees expressed by the users of a very popular social platform, Twitter. We analyse sentiment and the associated context of expressions in a vast collection of tweets related to the EU refugee crisis. Our study reveals a marginally higher proportion of negative sentiments vis-a-vis migrants and a large proportion of the negative sentiments is more reflected among the ordinary users. Users with many followers and non-governmental organisations (NGO) tend to tweet favourably about the topic, offsetting the distribution of negative sentiment. We opine that they can be encouraged to be more proactive in neutralising negative attitudes that may arise concerning similar incidences.