Robots learning a new manipulation task from a small amount of demonstrations are increasingly demanded in different workspaces. A classifier model assessing the quality of actions can predict the successful completion of a task, which can be used by intelligent agents for action-selection. This paper presents a novel classifier that learns to classify task completion only from a few demonstrations. We carry out a comprehensive comparison of different neural classifiers, e.g. fully connected-based, fully convolutional-based, sequence2sequence-based, and domain adaptation-based classification. We also present a new dataset including five robot manipulation tasks, which is publicly available. We compared the performances of our novel classifier and the existing models using our dataset and the MIME dataset. The results suggest domain adaptation and timing-based features improve success prediction. Our novel model, i.e. fully convolutional neural network with domain adaptation and timing features, achieves an average classification accuracy of 97.3\% and 95.5\% across tasks in both datasets whereas state-of-the-art classifiers without domain adaptation and timing-features only achieve 82.4\% and 90.3\%, respectively.