No, accusative case is used for the object of a sentence whether it is an animate or inanimate noun. The accusative form of masculine and neuter inanimate nouns is the same as their nominative forms, so that may have caused some confusion. However, feminine inanimate nouns which end in -а, like тарелка, are not the same in the nominative and accusative case.
OK, now I am replying to myself, LOL! But just want to say, when I went back to the exercise, I see that on this particular screen we did not get the turtle icon. So, hopefully, this word will pop up on other screens that offer the slow speech mode via the turtle. Sorry, DavidKestl1, for any confusion I may caused!
I have... statements have a different construction that does not use accusative case. у [genitive case] есть [nominative case]. Literally translated, у меня есть мама, would be "By me there is/exists mom." Mom, in this sentence, is not the grammatical direct object of the sentence and so is not in the accusative form.
In Я вижу тарелку, however, тарелку is the direct object and so must be in accusative form. "I see mom" would also use the accusative маму.
The subject (or nominative) is the word that comes before the verb. The object (or accusative) is the word that comes after it. Most words in Russian are the same for both of these forms but there are some exceptions, such as words ending in -а (or -я). These become -у (or -ю) in the accusative. Most feminine words work this way. So e.g.
The plate loves the table => Тарелка любит стол. But
The table loves the plate => Стол любит тарелку.