No, the difference is not just one of aspiration but of voiceless against voiced. But generally English consonants tend to be more aspired than their Russian counterparts.

You have to keep in mind that the hardening* of final consonants, which exists in Russian, does not exist in English. So it's much more likely that you pronounce a final b, d or g sound without voice by mistake, where English keeps it voiced.

* It is also important to note that in English "hard" and "soft" are mostly understood to be "voiceless" and "voiced" respectively, this does not refer to the concepts of hard and soft as they are in understood in the context of Russian. When a voiced consonant becomes voiceless it is called hardening.