Academic motivation is recognised as a key factor for academic success and wellbeing. Highly motivated students actively engage with academic activities and maintain good wellbeing. Despite the importance of motivation in education, its relationship with engagement and wellbeing remains to be evaluated. Accordingly, this study explored the relationships between motivation, engagement, self-criticism and self-compassion among UK education postgraduate students. Of 120 postgraduate students approached, 109 completed three self-report scales regarding those constructs. Correlation, regression and moderation analyses were performed. Intrinsic and extrinsic motivation were positively associated with engagement, whereas amotivation was negatively associated with it. Engagement positively predicted intrinsic motivation. Self-criticism and self-compassion moderated the pathway from extrinsic motivation to intrinsic motivation: higher self-criticism weakened the pathway, while higher self-compassion strengthened it. Findings suggest the importance of engagement in relation to cultivating intrinsic motivation of education students. Moreover, enhancing self-compassion and reducing self-criticism can help transfer extrinsic to intrinsic motivation.