What field are you looking to study in? Managers work well as professional references, as they can speak about your abilities from having supervised you at work. However for some universities/certain fields there will be a clear requirement for academic references, particularly if it's a research-focused course.
Academic references speak to your academic strengths/abilities, so if you've done well in a subject there's no harm reaching out to a previous teacher to see if they'd do an academic reference for you. You can always start your email off with an introduction - e.g. 'by way of introduction, I was a student in your subject of X in 20xx year, I received this grade for the subject...I am looking to study X in Y university, and Y university has requested an academic reference'...and so on. Teachers/lecturers are familiar with the concept of academic references and understand that students are often in a position of needing help.