Statistical learning, the process of extracting regularities from the environment, plays an essential role in many aspects of cognition, including speech segmentation and language acquisition. A key component of statistical learning in a linguistic context is the perceptual binding of adjacent individual units (e.g., syllables) into integrated composites (e.g., multisyllabic words). A second, conceptually dissociable component of statistical learning is the memory storage of these integrated representations. Here we examine whether these two dissociable components of statistical learning are differentially impacted by top-down, voluntary attentional resources. Learners' attention was either focused towards or diverted from a speech stream made up of repeating nonsense words. Building on our previous findings, we quantified the online perceptual binding of individual syllables into component words using an EEG-based neural entrainment measure. Following exposure, statistical learning was assessed using offline tests, sensitive to both perceptual binding and memory storage. Neural measures verified that our manipulation of selective attention successfully reduced limited-capacity resources to the speech stream. Diverting attention away from the speech stream did not alter neural entrainment to the component words or post-exposure familiarity ratings, but did impact performance on an indirect reaction-time based memory test. We conclude that theoretically dissociable components of statistically learning are differentially impacted by attention and top-down processing resources. A reduction in attention to the speech stream may impede memory storage of the component words. In contrast, the moment-by-moment perceptual binding of speech regularities can occur even while learners' attention is focused on a demanding concurrent task, and we found no evidence that selective attention modulates this process. These results suggest that learners can acquire basic statistical properties of language without directly focusing on the speech input, potentially opening up previously overlooked opportunities for language learning, particularly in adult learners.