That is no way to define Classical!
The Classical Period (narrow definition) is the period between the Baroque and the Romantic - say Haydn/Mozart/early Beethoven.
The genre of classical music is (vaguely) everything that is not folk music, popular music or Jazz. It is hard to find a clear dividing line though, and easier to point at particular attributes of one or other type of music: classical music is generally through-composed, and generally has a considerable degree of development; popular music (folk music was different) is now largely music that has been commodified by the corporations for the purpose of selling ever greater numbers of records (hence the requirement for it to be evanescent; and hence also their panic over the possibility of music being distributed without the sale of hardware).
Classical music can use whatever instruments are around - it is only the old-fashoined elitist view of "classical music", defined as the big romantics with a nod to the baroque in Bach and Handel, and moments of daring modernity with Elgar, that might claim a specific set of instruments as "classical" (essentially the symphony orchestra and the piano). Classical Music has included a wide range of modern percussion instruments - Stockhausen's Kontacte, Birtwistle's The Axe Manual, and Connolley's Night Thoughts are substantial examples that come to mind. It's not that classical music doesn't use the drum kit, but rather that popular music has focussed on a stylised form of it, as it has focused on a stylised format of songs and albums.
