The Euclid mission is expected to image millions of galaxies at high resolution, providing an extensive dataset with which to study galaxy evolution. Because galaxy morphology is both a fundamental parameter and one that is hard to determine for large samples, we investigate the application of deep learning in predicting the detailed morphologies of galaxies in Euclid using Zoobot, a convolutional neural network pretrained with 450 000 galaxies from the Galaxy Zoo project. We adapted Zoobot for use with emulated Euclid images generated based on Hubble Space Telescope COSMOS images and with labels provided by volunteers in the Galaxy Zoo: Hubble project. We experimented with different numbers of galaxies and various magnitude cuts during the training process. We demonstrate that the trained Zoobot model successfully measures detailed galaxy morphology in emulated Euclid images. It effectively predicts whether a galaxy has features and identifies and characterises various features, such as spiral arms, clumps, bars, discs, and central bulges. When compared to volunteer classifications, Zoobot achieves mean vote fraction deviations of less than 12% and an accuracy of above 91% for the confident volunteer classifications across most morphology types. However, the performance varies depending on the specific morphological class. For the global classes, such as disc or smooth galaxies, the mean deviations are less than 10%, with only 1000 training galaxies necessary to reach this performance. On the other hand, for more detailed structures and complex tasks, such as detecting and counting spiral arms or clumps, the deviations are slightly higher, of namely around 12% with 60 000 galaxies used for training. In order to enhance the performance on complex morphologies, we anticipate that a larger pool of labelled galaxies is needed, which could be obtained using crowd sourcing. We estimate that, with our model, the detailed morphology of approximately 800 million galaxies of the Euclid Wide Survey could be reliably measured and that approximately 230 million of these galaxies would display features. Finally, our findings imply that the model can be effectively adapted to new morphological labels. We demonstrate this adaptability by applying Zoobot to peculiar galaxies. In summary, our trained Zoobot CNN can readily predict morphological catalogues for Euclid images.