The adversarial impact of the Covid-19 pandemic has created a health crisis globally all over the world. This unprecedented crisis forced people to lockdown and changed almost every aspect of the regular activities of the people. Thus, the pandemic is also impacting everyone physically, mentally, and economically, and it, therefore, is paramount to analyze and understand emotional responses during the crisis affecting mental health. Negative emotional responses at fine-grained labels like anger and fear during the crisis might also lead to irreversible socio-economic damages. In this work, we develop a neural network model and train it using manually labeled data to detect various emotions at fine-grained labels in the Covid-19 tweets automatically. We present a manually labeled tweets dataset on COVID-19 emotional responses along with regular tweets data. We created a custom Q&A roBERTa model to extract phrases from the tweets that are primarily responsible for the corresponding emotions. None of the existing datasets and work currently provide the selected words or phrases denoting the reason for the corresponding emotions. Our classification model outperforms other systems and achieves a Jaccard score of 0.6475 with an accuracy of 0.8951. The custom RoBERTa Q&A model outperforms other models by achieving a Jaccard score of 0.7865. Further, we present a historical emotion analysis using COVID-19 tweets over the USA including each state level analysis. © 2021 Elsevier B.V. All rights reserved.