The use of apple pomace flour (APF) as a fibre enrichment strategy was investigated. The aim of this study was to evaluate consumers’ response to intrinsic and extrinsic properties of a bakery premix product when using APF. Apple pomace, a by-product from the juice industry, was dried and ground. APF is high in carbohydrates (47.47%) and fibre (38.48%), and it was used to partially substitute wheat flour and sugar in a cake premix. Acceptability, health, and nutrition questions were evaluated with and without information in terms of regular and fibre-enriched cake. The regular cake score was not affected by information, while the enriched cake’s score increased with information. Three clusters were identified. Cluster 1 (29%) showed high liking scores for regular cake, cluster 2 (31%) for the fibre-enriched cake, and cluster 3 (40%) showed similar liking for both. Consumers described the samples and ideal cake using a check-all-that-apply (CATA) questionnaire. Penalty analyses explained differences in acceptability among consumers. Healthiness, tastiness, and fibre content were the main reasons to buy the enriched cake for cluster 2; taste for consumers in cluster 1; and healthiness and taste for consumers in cluster 3. APF as a functional ingredient may be a consumers’ choice as a sustainable use of apple pomace.