I don't think so. Is there a difference in other languages?
It's a difference in other varieties of English, actually. One of my phonetics/phonology profs in undergrad was a native speaker of Indian English, and he had some minimal pairs (or near-minimal pairs). He tried to convince me that they were phonetically distinguishable, but I couldn't hear the difference at all. Not just the way I can't hear the difference between [ɑ] and [ɔ], where I feel like I can hear a phonetic difference but it's completely uninformative to my grammar, but, like, I just couldn't hear anything. I think it's still maintained in other Englishes, too.
So, sorry, Xahar, you just have to memorize that [ʌ] happens in stressed syllables and [ə] in unstressed ones! At least your prof isn't penalizing you for not distinguishing /ɑ/ and /ɔ/
