For the class of mixed channels decomposed into stationary memoryless channels, single-letter characterizations of the $\varepsilon$-capacity have not been known except for restricted classes of channels such as the regular decomposable channel introduced by Winkelbauer. This paper gives single-letter characterizations of $\varepsilon$-capacity for mixed channels decomposed into at most countably many memoryless channels with a finite input alphabet and a general output alphabet with/without cost constraints. It is shown that a given characterization reduces to the one for the channel capacity given by Ahlswede when $\varepsilon$ is zero. In the proof of the coding theorem, the meta converse bound, originally given by Polyanskiy, Poor and Verdú, is particularized for the mixed channel decomposed into general component channels.