"Classical music" has two slightly different meanings. It usually means orchestral music in the European high-art tradition: Bach, Mozart, Beethoven, Tchaikovsky, Prokofiev, Bartok. To people in the field, it means a specific period and style that precedes the "Romantic" period. "A classic" is not normally used when referring to pieces of classical music. "The classics" sometimes refers to the literature of Greece and Rome from about 600 BCE to 600 CE. "A classic" often means "a work which is expected to endure." In popular culture, "a classic" often means "a work that is now old enough to judge as being great and lasting." Walt Disney's animated "Snow White" 1937 is a classic of animation. Chuck Berry's "Sweet Little Sixteen" (1958) is a classic of rock 'n' roll. Isaac Asimov's "I, Robot" is a science fiction classic. Roald Dahl's "James and the Giant Peach" (1961) is a classic of children's literature. However, Beethoven's Fifth Symphony is a great work of classical music.

If you mean music written by Beethoven, Bach, Brahms etc., the correct phrase would be classical music. The word 'classic' could be applied to any sort of music e.g. classic tracks from The Beatles.